iq test scores are normally distributed with a mean of 100 and a standard deviation of 15. an individual's iq score is found to be 90. find the z-score corresponding to this value.

Answers

Answer 1

The Z score of the individual with IQ 90 is -0.67.

It is given that the scores are Normally distributed.

The mean given is 100 while the standard deviation is 15.

Let the IQ distribution be X.

Hence X follows a Normal distribution X~N(100, 225)

where

100 = mean

225 = standard deviation

To find the Z score we need to convert the following into the standard normal distribution.

To do that we need to follow

Z = ((x - μ) / σ)

here

μ = mean of the distribution = 100

σ = standard deviation of the distribution = 15

x = 90

Hence the Z score is

Z = (90 - 100) / 15

= -10/15

= -0.67

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Related Questions

the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)

Answers

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.

acc to our question-,

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

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simplify the following

Answers

Answer: 12⋅|x3|−512√⋅|3|

PLEASR GIVE BRAINLIEST THANK YOU VERY MUCH!!!

true or false? finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely.

Answers

It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".

What is standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.

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During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2

Answers

The values are not equivalent to 2.2 include

2.6 - 0.6

1.8 + 2.5

What is an expression?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, 2.6 - 0.6 will be:

= 2.6 - 0.6

= 2.0

Also, 1.8 + 2.5 will be:

= 1.8 + 2.5

= 4.3

Therefore, they're not equivalent to 2.2

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Complete question

During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2

1.2 + 1.0

2.6 - 0.6

0.9 + 1.3

1.8 + 2.5

Which of The following Best describes the transformation of Y=x^2 so that the resulting equation is as follows?
Y=(x-3)^2+4

Answers

By using the concept of translation, it can be inferred that

The graph of the equation is translated 3 units to the left and 4 units down

What is translation?

Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.

The given equation is

[tex]y = (x +3)^2 + 4[/tex]

This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.

So the first option is correct.

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Find the equation of the linear function represented by the table below in slope-
intercept form.

Answers

The equation of the linear function represented by the table would be y = 4x - 1.

What is the slope-intercept form of the line?

When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula

                               y = mx + c.

The y value of the y-intercept point is represented by c in the formula.

By using the given table,

for x = 0 , y = -1

so by using the slope-intercept form of the line, we can write

              y = mx + c

              -1 = m(0) + c

               c = -1 ----------(I)

Then for x = 1, y = 3

again by using the slope-intercept form of the line, we can write

                  y = mx + c

                 3 = m(1) + (-1)  -----from (I)

                  3 = m - 1

             ⇒ m = 3 + 1

             ⇒ m = 4 -----------(II)

Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line

                     y = 4x - 1

Hence, the equation of the linear function represented by the table would be y = 4x - 1.

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a group of 350 people includes 187 play the flute, 172 play the clarinet, and 47 both the flute and the clarinet. a person is selected at random. 1. what is the probability that he/she plays the clarinet but not the flute? a. 0.4213 b. 0.3571 c. 0.7812 d. 0.4587 e. 0.2743 2. what is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7571 e. 0.3645 3. what is the probability that he/she plays at most one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.8657

Answers

Using probability concepts, we calculated that the likelihood that the person plays the clarinet but not the flute is 0.2743.

What is conditional probability?

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.

Here,

Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.

There are 47 people who can play both the clarinet and the flute.

As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.

Probability(P),

P=( 125 / 350)

P=0.2743.

Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.

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What is the value of 5.53?

Answers

The value of 3 in 5.53 is 3 hundredths.

What is place value?

It is important to note that place values can be defined as the value that's represented by a digit based on the position that it takes. In mathematics, place value refers to the position or location of a digit in a number.

Each digit has a specific place in a number. The position of each digit will be expanded when we represent the number in general form. Those positions begin with a unit place, also known as one's position.

In this case, we want to know the value of 3 in 5.53. It should be noted that the first 5 is 5 ones, the second 5 is 5 tenths and the 3 is 3 hundredths.

Therefore, it's 3 hundredths.

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Complete question

What is the value of 3 in 5.53?

Evaluate -7(x - 4y) when x = -4 and y = -6.
A 140
B 52
C-28
D-140​

Answers

Answer: D

Step-by-step explanation:

Take the equation and substitute the variables for the numbers given

-7(-4-4(-6))=-140

Hope this helps :)

Amir want to proportionally increae the ize of a photo to create a poter for hi room. The ize of the original photo i hown. Complete the tatement and then anwer the quetion to repreent way that Amir can increae the ize of hi photo

Answers

The height of the poster is 20 inches.

The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.

The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".

30 = k*6

k = 30/6

k = 5

Hence, the poster is scaled up by a factor of five.

H = k*4

H = 5*4

H = 20

Hence, the height of the scaled-up poster is 20 inches.

The complete question is given below.

Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?

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An elevator ascends at a rate of 29.6 feet per second. If a building is 1,450 feet tall, about how long would it take for the elevator to travel from the ground floor to the roof?

A. 0.49 minutes
B. 0.82 minutes
C. 4.9 minutes
D. 8.2 minutes

Answers

It’s B. You would divide 1,450 ft by 29.6 ft which is 49 (rounded). Then multiply 1 second with that 49 which would be 49 seconds. Convert 49 second to minutes which is then .82 minutes.

Which expression is the factored form of−4.5n+3?

Responses

A. −3(1.5n−1)

B. −1.5(3n+2)

C. −1.5(−3n+2)

D. −3(1.5n+1)

Answers

An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

In this question we have been given an expression -4.5n + 3

We need to identify an expression which is factored form of given expression.

If we simplify the factored form then it must be a give expression.

consider ,A. −3(1.5n−1)

= -4.5n + 3

consider an expression B. −1.5(3n+2)

= -4.5n - 3

consider C. −1.5(−3n+2)

= 4.5n - 3

consider D. −3(1.5n+1)

= -4.5n - 3

Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

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reduce with all steps​

Answers

Answer
40+44 / 2
84 / 2
42

new york city is the most expensive city in the united states for lodging. the mean hotel room rate is $204 per night. assume that the room rates are normally distributed with a standard deviation of $55. answers to 3 decimals. what is the probability of more than $225?

Answers

The probability of more than $225 is 0.35197.

Here we need to find the probability of more than $225.

We need to calculate the z-score associated with x = $225

Z(score) = 225 - 204 / 55

= 0.381818

z(score) = 0.38

For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.

Here we have to find the values greater than this value:

P(z > 0.38) = 1 - P (z < 0.38)

P( z > 0.38) = 0.35197

So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.

Therefore the probability is 0.35197.

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The map shows a portion of downtown Mapledale. Main Street and 2nd Avenue are parallel. Use the map to answer each question. ​ Question​ Angle​ ​Which angle is an alternate exterior angle to angle 8? ​ Which angle is a same-side interior angle to angle 2?​ ​ Which angle is a corresponding angle to angle 3?​

Answers

a. Angle 4 is an alternate exterior angles to angle 8.

b. Angle 3 is same-side interior angle to angle 2.

c. Angle 1 is corresponding angles to angle 3.

What are Corresponding Angles?

Corresponding angles are located on the same corner and on the same side of a transversal.

For example, in the given image below, angles 1 and 3 are corresponding angles.

What are Alternate Exterior Angles?

Alternate exterior angles are any two exterior angles that lie on two different parallel lines but on alternate sides of the transversal that crosses the two parallel lines.

For example, in the image given, angles 8 and 4 are alternate exterior angles.

What are Same-side Interior Angles?

Same-side interior angles are interior angles that are located on the same side of the transversal but on different parallel lines that the transversal cuts across.

For example, angles 2 and 3 are same-side interior angles as seen in the given image.

What are Corresponding Angles?

Corresponding angles are located on the same corner and on the same side of a transversal.

For example, in the given image below, angles 1 and 3 are corresponding angles.

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PLEASE HELP!

3. In a survey of 1000 eligible voters selected at random, it was found that 8% had a college degree. Additionally it was found that 80% of those who had a college degree voted in the last presidential election. Whereas 55% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random voted. Draw a diagram to represent this situation.




a) If you randomly chose an eligible voter from this group, what is that probability that they have a degree and did not vote?





b) If you randomly chose an eligible voter from this group, what is the probability that they voted?




c) If you randomly chose a person who voted in the presidential election, what is the probability that they had a college degree?​

Answers

hello, i'm sorry but i can't graph the diagram but here are the answers for a-c :)

A. 8%

B. 39.6%

C. 58.4%

step by step:

A. Calculation to determine the probability of The voter had a college degree and voted in the last presidential election.

P = 80/1,000

P=0.08*100

P=8%

Therefore the probability of The voter had a college degree and voted in the last presidential election will be 8%

B. Calculation to determine the probability of The voter did not have a college degree and did not vote in the last presidential election.

P =396/1000

P=0.396*100

P=39.6%

Therefore the probability of The voter did not have a college degree and did not vote in the last presidential election will be 39.6%

C. Calculation to determine the probability if The voter voted in the last presidential election.

P = 584/1,000

P=0.584*100

P=58.4%

Therefore the probability if The voter voted in the last presidential election will be 58.4%

answer this and u a big W if u dont ur a L

Answers

Answer:

Part A. (4,5)

Part B. (9,7)

Step-by-step explanation:

Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.



Chelsea has final exams in calculus, physics, and history.
She has up to 25 hours to study for exams. She plans to
study history for 2 hours. She needs to spend at least 7
hours studying for calculus, but over 14 is too much.
She hopes to spend between 8 and 12 hours on physics.
Write and graph a system of inequalities to represent
the situation.

Answers

Answer:

x-variable    y-variable    Inequalities

calculus       physics        7≤x≤14

                                        8≤y≤12

                                        x+y≤23

Step-by-step explanation:

Find the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7).​

Answers

The equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49

The equation of the parallel line is given

6x + y = -8

y = -8 -6x

y = -6x - 8

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Comparing the equation

Slope of the line m = -6

The slope of the all the parallel lines will be equal

Then line is passing through the point (7, 7)

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values in the equation

y-7 = -6(x-7)

y - 7 = -6x + 42

y = -6x +42 +7

y = -6x + 49

Hence, the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49

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An isosceles right triangle has a hypotenuse length that can be modeled with the function . the combined length of the legs can be modeled with the function l(x) = 2x. which function, p(x), can be used to find the perimeter of the triangle?

Answers

The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.

A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be  L(x) = 2x. Using this information the perimeter of the triangle comes out to be,

P(x) = h(x) + L(x).

P(x) =  x√2 + 2x

Hence the perimeter of the triangle comes out to be P(x) =  x√2 + 2x

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My science class is pretty small. There are just 18 students in the class. My
teacher, Ms. Microbe, has an unusual system for pairing us up for labs. She
has given each of us a number from 1 through 18, and on lab days, she pulls
our numbers out of a bag to determine who is paired with whom. When we
did our last lab, I happened to notice that the sum of each person's number
with his/her lab, partner's number was a perfect square!
How were the partners assigned?

Answers

The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9).

Square numbers:

A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.

For example:

Square of 2 = 4

Square of 3 = 9

Square of 4 = 16

           

Here we have  

A science class is pretty small

There are just 18 students in the class.

The teacher gave each of them numbers from 1 through 18 on lab days

Start from 1 and find by adding which number we will get a square number

Here  1 + 15 = 16

2 + 14 = 16

3 + 13 = 16

4 + 12 = 16

5 + 11 = 16

6 + 10 =16

After the above combinations, the remaining numbers are

7, 8, 9, 16, 17, 18          

which can be added as given below to get square number 25  

=>  18+7=25

=>  17+8=25

=>  16+9=25  

Therefore,

The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9)  

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Segment RS is reflected over the line y = and then translated by (x +3, y + 4). The resulting segment
R" S" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
R=
S =

Answers

Answer:

-1,-2

Step-by-step explanation:

get the x and y value and combine the coordinates using the slope formula

point A is located at (-2,-6) on the coordinate plane. Point A is reflected over the y-axis to create point A’. What ordered pair describes the location of A’?

Answers

The ordered pair coordinates of A' are (2, -6) if A is reflected over the y-axis.

What are transformations?

The transformation, or f: X → X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.

The coordinates of A are (-2, -6).

Point A is reflected over the y- axis to create point A'

(x, y) → (-x,y)

A (-2, -6) → A' (- (-2), -6))

So, the coordinates of A' are (2, -6).

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The Tran family and the Campbell family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 35 L per hour. The water output rate for the Campbell family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1925 L. How long was each sprinkler used?

Answers

The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The water output rate for the Tran family's sprinkler was 35 L per hour.

The water output rate for the Campbell family's sprinkler was 25 L per hour.

And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.

Now,

Let time in hours for the Tran family's sprinkler = t

And, The time in hours for the Campbell family's sprinkler = 65 - t

So, We can formulate by the given condition,

⇒ 35t + 25 (65 - t) = 1925

Solve for t as;

⇒ 35t + 25 (65 - t) = 1925

⇒ 35t + 1625 - 25t = 1925

⇒ 10t + 1625 = 1925

⇒ 10t = 1925 - 1625

⇒ 10t = 300

⇒ t = 30

Thus, The time in hours for the Tran family's sprinkler = t

                                                                                   = 30 hours

And, The time in hours for the Campbell family's sprinkler = 65 - t

                                                                                          = 65 - 30

                                                                                          = 35 hours.

Therefore, we get;

The time in hours for the Tran family's sprinkler will be 30 hours.

The time in hours for the Campbell family's sprinkler will be 35 hours.

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Ms. Galindo’s class has adopted two equal sections of a highway to keep clean. The combined length of the two sections is
6/8

of a mile. How long is each section?

Answers

Each section of a highway has length of 1.5 miles.

In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.

We need to find the length of each section.

Let each section measures x mile.

The combined length of the two sections is 6/8 of a mile.

So, we get an equation x + x = 6/8

We solve above equation to find the value of x.

2x = 6/8

x = (6/8) / 2

x = 6/4

x = 1.5

Therefore, each section of a highway has length of 1.5 miles.

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a new car model is available with 5 choices of color, 3 choices of transmission and 4 types of interior. how many different variations of this model car are possible?

Answers

In 120 different variations of this model car are possible.

Define multiplication.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.

Given,

There are five different ways to choose a car's color.

3 different car transmission selection options are available.

There are four different interior automobile selection options.

There are two different ways to pick a car's engine.

The potential number of car variations is thus:

Multiplying:

5 × 3 × 4× 2

120

In 120 different variations of this model car are possible.

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a) 110⁰
b) 70⁰
c) 73⁰
d) 115⁰

Answers

Answer:I think is am B

Step-by-step explanation:

Step-by-step explanation:

(5x)°+(3x+4)°=180°

5x+3x+4=180

8x=176

x=22

D=5x

D=110°

Angles RTG and GTU are adjacent angles. If m∠RTG=5.8° and m∠GTU=113.6°, what is m∠RTU in degrees?

Answers

If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.

∠RTU = ∠RTG + ∠GTU

∠RTU = 5.8° + 113.6°

∠RTU = 119.4°

The measure of the angle ∠RTU will be 119.4°.

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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Given:-16=m-18;Prove:m=10

Answers

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

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