Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from student to student according to a Normal distribution with mean 0.07 ans standard deviation 0.01.
1. The middle 95% of students who drink five beers have a BAC between
a. 0.06 and 0.08 b. 0.05 and 0.09 c. 0.04 and 0.10 d. 0.03 and 0.11
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
Answer:
1. b. 0.05 and 0.09
2. d. 16%
3. a. 0.15%
Step-by-step explanation:
Given that :
mean = 0.07
standard deviation = 0.01
Confidence interval = 95%
The level of significance ∝= 1 - 0.95 = 0.05
At 0.05 level of significance,
critical value for [tex]z_{\alpha/2} = z_{0.05/2}[/tex]
critical value for [tex]z_{0.025}[/tex] = 1.96
Confidence interval = [tex]\mathtt{\mu \pm ( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{\mu -( {z} \times{\sigma})}[/tex]
Upper Limit = [tex]\mathtt{\mu +( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{0.07 - ({1.96} \times {0.01})}[/tex]
Upper limit = [tex]\mathtt{0.07 + ({1.96} \times {0.01})}[/tex]
Lower limit = 0.07 - 0.0196
Upper limit = 0.07 + 0.0196
Lower limit = 0.0504 [tex]\simeq[/tex] 0.05
Upper limit = 0.0896 [tex]\simeq[/tex] 0.09
The confidence interval of 95% is ( 0.05, 0.09)
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
[tex]P(X> 0.08) = P(\dfrac{0.08 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.08 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.01}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > 1 )[/tex]
[tex]P(X> 0.08) = 1- P(z < 1 )[/tex]
P(X > 0.08) = 1 - 0.8413
P(X > 0.08) = 0.1587
P(X > 0.08) [tex]\simeq[/tex] 16%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
[tex]P(X> 0.10) = P(\dfrac{0.10 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.10 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.03}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > 3)[/tex]
[tex]P(X> 0.10) = 1- P(z < 3 )[/tex]
P(X > 0.10) = 1 - 0.9987
P(X > 0.08) = 0.0013
P(X > 0.08) [tex]\simeq[/tex] 0.15% which is the closet value to 0.0013
You have found the following ages (in years) of all 666 lions at your local zoo: 13,2,1,5,2,7 What is the average age of the lions at your zoo? What is the standard deviation? Average age: _____ years old Standard deviation: ____ years
Answer:
[tex]Mean = 5[/tex]
[tex]S_x = 4.123[/tex]
Step-by-step explanation:
Given
Number of Lions, n: 6
Ages: 13, 2, 1, 5, 2, 7
Required
Determine the:
1. Mean
2. Standard Deviation
Mean is calculated as;
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]Mean = \frac{13+2+1+5+2+7}{6}[/tex]
[tex]Mean = \frac{30}{6}[/tex]
[tex]Mean = 5[/tex]
Standard Deviation is calculated as follows
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{N}}[/tex]
Where Mx represent mean
Substitute values for x, Mean and Land
[tex]S_x = \sqrt{\frac{(13 - 5)^2+(2 - 5)^2+(1 - 5)^2+(5 - 5)^2+(2 - 5)^2+(7 - 5)^2}{6}}[/tex]
[tex]S_x = \sqrt{\frac{(8)^2+(- 3)^2+(-4)^2+(0)^2+(-3)^2+(2)^2}{6}}[/tex]
[tex]S_x = \sqrt\frac{64+9+16+0+9+4}{6}}[/tex]
[tex]S_x = \sqrt\frac{102}{6}}[/tex]
[tex]S_x = \sqrt{17}[/tex]
[tex]S_x = 4.123[/tex]
The mean and standard deviation is 5 and 4.123 respectively
We want to find the mean or average and the standard deviation of the given set.
The average age is 5 years old and the standard deviation is 4.52 years old.
We know that for a general set of N elements {x₁, x₂, ..., xₙ} the average or mean is given by:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
And the standard deviation is given by:
[tex]S = \sqrt{\frac{(x_1 - M)^2 + ... + (x_n - M)^2}{N - 1}[/tex]
The given set is:
{13, 2, 1, 5, 2, 7}
Now we just need to use the two given formulas for our set.
The mean is:
[tex]M = \frac{13 + 2 + 1+ 5 + 2 +7}{6} = 5[/tex]
And the standard deviation is:
[tex]S = \sqrt{\frac{(13 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (7 - 5)^2}{6 - 1} } = 4.52[/tex]
So the average age is 5 years old and the standard deviation is 4.52 years old.
If you want to learn more you can read:
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The perimeter of a park is 300 feet the length of the park is 50 feet longer than the width. Find the length
Answer:
55.41 feet
Step-by-step explanation:
Let the width be x.
ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet
Aidan has four cards with +, -, x, ÷ printed on them.
He inserts them between the five numbers 5, 4, 3, 2 and 1 to form the expression 5 + 4 x 3 -2 , which the value 15.
Emma says:
"Aidan put the operation in the order +, -, x, ÷.
If I place the operation cards in a different order between the number 5, 4, 3, 2, 1. I can make the value equal to 19."
Which operation would Emma do first?
9514 1404 393
Answer:
multiply (×)
Step-by-step explanation:
5 ×4 - 3 +2 ÷1 = 19
Emma would place the multiply (×) operation first.
If sin∠M = cos∠N and m∠N = 30°, what is the measure of ∠M?
Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
The formula v=at +16t² is used in mechanics.Rewrite to nake a the subject and find it's value when v=27 and t=4
Answer:
[tex]v = at + 16 {t}^{2} \\ v - 16 {t}^{2} = at \\ \frac{v - 16 {t}^{2} }{t} = a \\ (27 - 16 \times {4}^{2}) \div 4 = a\\ \frac{27 - 256}{4} = a\\ \frac{ - 229}{4} = - 57.25 \\ thank \: you[/tex]
Write down the name of the shape for question D. Please help!
Step-by-step explanation:
thats shape is a delta
:)
Answer:
arrow head
Step-by-step explanation:
If the discriminant of a quadratic equation is equal to -8 , which statement describes the roots?
Answer: There are no real number roots (the two roots are complex or imaginary)
The discriminant D = b^2 - 4ac tells us the nature of the roots for any quadratic in the form ax^2+bx+c = 0
There are three cases
If D < 0, then there are no real number roots and the roots are complex numbers.If D = 0, then we have one real number root. The root is repeated twice so it's considered a double root. This root is rational if a,b,c are rational.If D > 0, then we get two different real number roots. Each root is rational if D is a perfect square and a,b,c are rational.Bianca is styling hair and makeup for the upcoming dance at her high school. She charges $51 for hair and $35 for makeup. Identify the expression that can be used to represent this situation. (2 points)
86hm
51h(35m)
51h + 35m
A researcher is interested in determining whether various stimulant drugs improve maze leaming performance in rats. To find out, the researcher recruits 16 rats and assigns 4 rats to one of 4 research conditions: caffeine, nicotine, cocaine, placebo. Each rat completes the maze once and in only one research condition and is timed; time to complete the maze is the researcher's measure of performance. Answer the following questions considering the data below (alpha)
Caffeine Nicotine Cocaine Placebo
30.00 45.00 30.00 60.00
45.00 75.00 30.00 75.00
45.00 60.00 60,00 60.00
45.00 45.00 30.00
What is the dependent variable in this study?
a. Drug condition
b. Time to complete maze
c. Number of rats
d. Research conditions
16. What analysis should be used to answer the researcher's question?
a. One-way between-subjects (a.ka. independent-samples) ANOVA
b. One-way within-subjects (a.k.a. dependent-samples, repeated-measures) ANOVA
c. Factorial ANOVA
d. T-test 17.
What is the Null hypothesis for this analysis?
a. There will be no difference between any group means
b. Maze performance will get worse with stimulants
c. Maze performance of at least one group will differ from typing of at least one other group
d. Maze performance on placebo will be worse than on all drugs
What are the degrees of freedom for the numerator of the F-ratio?
2
3
8
11
What are the degrees of freedom for the denominator of the F-ratio?
2
3
8
11
What is the critical F value for this analysis?
a. 3.49
b. 4.07
c. 6.04
d. 19.00
What is the SSbetween-groups value?
a. 425.00
b. 1181.25
c. 2517.19
d. 3698.44
What is the SSwithin value?
Answer:
1) The dependent variable is : time to complete the maze
2) The analysis used should be : One -way within-subjects ANOVA ( B )
3) Null hypothesis is ; There will be no difference between any group means
4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
5) degree of freedom for the denominator = 11
6) critical F value = 3.49
Step-by-step explanation:
The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .
The analysis used should be : One -way within-subjects ANOVA ( B )
Null hypothesis is ; There will be no difference between any group means
Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11
The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F - table the critical value would be 3.49
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
Find the final amount of money in an account if $7, 200 is deposited at 2.5 % interest compounded
quarterly (every 3 months) and the money is left for 9 years.
The final amount is $
Round answer to 2 decimal places
The final amount is $7,615.27
A = P(1 + r/n)^t
Where,
A = Final amount
P = principal = $7, 200
r = interest rate = 2.5% = 0.025
n = number of periods = 4
t = time = 9 years
A = P(1 + r/n)^t
= 7,200(1 + 0.025/4)^9
= 7,200(1 + 0.00625)^9
= 7,200(1.00625)^9
= 7,200(1.0576769512798)
= 7,615.2740492152
Approximately,
A = $7,615.27
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How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145
Answer:
Mean: 169.4
Median: 171
Mode: 181
Step-by-step explanation:
I first sorted the numbers by value, least to greatest.
145 147 153 153 167 170 170 172 181 181 181 182 185 185
We can see that 181 occurs the most, 3 times, so it's the mode.
The median of this set will be the middle number(s).
When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.
We can add all the numbers and divide by 14 to get the mean.
[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]
Hope this helped!
Help please!! Simplify the following expression
*4 + 3x3 - 2x - 5x2 - X+ x2 + x +1+7x4
O A. 8x4 +5x2 + 4x2 + 0x+1
B. 8x4 +5x + 4x2 +1
C. 8x4 + x2 - 4x + 0x
D. 8x4 + x2 - 4x2 +1
━━━━━━━☆☆━━━━━━━
▹ Answer
D. 8x⁴ + x³ - 4x² + 1
▹ Step-by-Step Explanation
Remove the opposites:
x⁴ + 3x³ - 2x³ - 5x² + x² + 1 + 7x²
Collect like terms:
8x⁴ + 3x³ - 2x³ - 5x² + x² + 1
8x⁴ + x³ - 5x² + x² + 1
8x⁴ + x³ - 4x² + 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
Fifteen chaperones went on a field trip with 225 students. Which fraction represents the number of chaperones to students on the field trip
Answer:
15/225
Step-by-step explanation:
The number of chaperones for the group of students can be represented with a ratio - 15:225 or 15/225.
Because there are 15 chaperones for the 225 students, you can state what the ratio does - for every 225 students, there are 15 chaperones.
However, 15/225 can be reduced to 1/15, so for every 15 students, there is 1 chaperone.
(Score for Question 1: ____ of 5 points)
1. The equation of a circle is x2 + y2 - 4x + 2y - 11 = 0. What are the center and the radius of the circle?
Show your work
Answer:)
Answer:
The center of the circle:
(2, -1)
The radius of the circle:
r = 4
Step-by-step explanation:
The first step is to complete the square on both x and y:
x^2 + y^2 -4x + 2y - 11 = 0
x^2 -4x +y^2 +2y = 11
We determine c1 to complete the square on x:
c1 = (b/2)^2
c1 = (-4/2)^2 = 4
We then determine c2 to complete the square on y:
c2 = (2/2)^2 = 1
The equation of the circle is then re-written as:
x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1
We then factorize the expressions in x and y separately:
(x-2)^2 + (y +1)^2 = 16
The center of the circle is thus:
(2, -1)
The radius is the square root of 16:
r = 4
Answer:
center : (2, -1)
radius : r = 4
Step-by-step explanation:
WILL GIVE BRAINLIEST
Use the distributive property.
5(2x + 7) = [ ? ]x + [ ]
Answer:
10x +35
Step-by-step explanation:
5(2x+7) = 5*2x + 5*7 = 10x+35
Answer:
10, 35.
Step-by-step explanation:
5(2x + 7)
= 5^2x + 5*7
= 10x + 35
in the diagram, POS,QOT and ROU are straight lines. find the value of x.
==========================================
Explanation:
Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees
(angle POU) + (angle UOT) + (angle TOS) = 180
4x + x + 40 = 180
5x + 40 = 180
5x = 180-40
5x = 140
x = 140/5
x = 28
Side note: if x = 28, then 4x = 4*28 = 112.
We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.
A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at a photograph of a 6-foot tall man with a shadow that is 3.5 feet. Find the angle at which the sun is hitting the ground.
Answer:
The angle [tex]\theta[/tex] at which the sun is hitting the ground is:
[tex]\theta\approx 59.74^o[/tex]
Step-by-step explanation:
You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.
The use the tangent function to find the angle that the sun's rays make with the ground:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{6}{3.5} \\\theta=arctan(\frac{6}{3.5})\\\theta\approx 59.74^o[/tex]
Multiply the following complex numbers:
(7+2i)(2+3i)
Please don’t guess
Answer:
14 + 25l + 6l^2
Step-by-step explanation:
(7 + 2i) (2 + 3i)
=> 14 + 4l + 21l + 6l^2
=> 14 + 25l + 6l^2
This is the correct answer
Shane plants a 6-inch tomato plant in his garden. The plant grows by about 12% per week for several months. Which function definition represents the height of the tomato plant (in inches) as a function of the number of weeks, t since the tomato plant was planted?
Answer:
[tex]f(t)=6(1.12^t)[/tex]
Step-by-step explanation:
every week the plant grows by 12%, so the ratio is 1.12. the original height of the plant is 6. f(x)=a(b^x) such that a=6, b=1.12, and x=t
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
m=3*sqrt(2) and n=3
Step-by-step explanation:
tan(45)=3/n
1=3/n, n=3. As it's a right angled triangle, 3^2+3^2=m^2, m=3*sqrt(2)
Help with number 50 please. Thanks.
Answer:
[tex] d = 7 + 3\sqrt{3} [/tex] and
[tex] d = 7 - 3\sqrt{3} [/tex]
Step-by-step explanation:
To solve the equation, [tex] d^2 - 14d - 22 = 0 [/tex], using the quadratic formula,
Recall: quadratic formula = [tex] \frac{-b ± \sqrt{b^2 - 4ac}}{2a} [/tex]
Where,
a = 1
b = -14
c = 22
Plug in your values into the formula and solve:
[tex] \frac{-(-14) ± \sqrt{(-14)^2 - 4(1)(22)}}{2(1)} [/tex]
[tex] \frac{14 ± \sqrt{196 - 88}}{2} [/tex]
[tex] \frac{14 ± \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 + \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 + 6\sqrt{3}}{2} [/tex]
[tex] d = (\frac{2(7 + 3\sqrt{3})}{2} [/tex]
[tex] d = 7 + 3\sqrt{3} [/tex]
And
[tex] d = \frac{14 - \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 - 6\sqrt{3}}{2} [/tex]
[tex] d = (\frac{2(7 - 3\sqrt{3})}{2} [/tex]
[tex] d = 7 - 3\sqrt{3} [/tex]
if 10x=1/0.001 find the value of x
[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]
Turn over the decimal[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]
[tex]\\ \sf\longmapsto 10x=1000[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]
[tex]\\ \sf\longmapsto x=100[/tex]
100 points for whoever can prove this geometry problem!!!! PLS HELP ME!!!!!!
Answer:
Let the chord- part of VC inside smaller circle be a, and same of CU be b.
According to intersecting secants theorem we have:
CI * (CI + a) = CJ * (CJ + b)and
VC *(CI + a) = CU * (CJ + b)From the second equation we get:
CU = VC * (CI + a) / (CJ + b)From the first equation we get:
CI + a = CJ * (CJ + b) / CI,substitute this into the second equation:
CU = VC * CJ * (CJ + b) / CI * 1/ (CJ + b)CU = VC * CJ / CICU * CI = VC * CJProved
Which regular polygon has a rotation of 240 degree to carry the polygon onto itself?
Equilateral triangle
Octagon
Rectangle
Pentagon
The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is an B. Octagon.
What is an Octagon?This refers to an eight-sided polygon that has eight angles and is used in geometry.
Hence, we can see that an octagon, can be rotated to 240 degrees and when this is done, it is able to carry itself which cannot be done by others as other polygons would need 360 degrees to carry themselves.
Read more about polygons here:
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Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one head. Which of the following sets of elements are included in the sample space
HHTHTTTTHTTTTHTHHHTHHHTH
List the elements of the given event. (Select all that apply.)
HHT
HTT
TTH
TTT
THT
HHH
THH
HTH
List the elements of the given event. (select all that apply)
HTT
TTH
HTH
THH
THT
HHH
TTT
HHT
Answer:
Even set = {HTT, THT, TTH, TTT}
Step-by-step explanation:
We are given that three coins are tossed; the result is at most one head.
And we have to find the sets of elements that are included in the sample space.
Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.
Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.
So, the sample space so formed is;
S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}
Now, our event is at most one head. So, the sample space for the favorable event is given by;
Even set = {HTT, THT, TTH, TTT}
In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.
In a zoo there are 6 orang-utans for every 3 baboons. There are 27 orang-utans and baboons altogether. How many are orang-utans?
Answer:
18
Step-by-step explanation:
Okay first we know that for every one baboon there is 2 orang-utans (6 / 3 = 2)
So, I like to play the guess and check:
Lets just use the numbers 12 orang-utans and 6 baboons. We know that those two don't equal 27, so thats not it.
Now we can have 18 orang-utans and 9 baboons. 18 + 9 = 27, which means there are 18 orang-utans.
Hope this helps, and have a good day.
Agyappng is three times as old as Atsu .three years ago ,he was four times as old as Atsu ..how old is each boy now
9514 1404 393
Answer:
Atsu is 9Agyappng is 27Step-by-step explanation:
Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...
(3x -3) = 4(x -3)
9 = x . . . . . . . . . . . . add 12-3x
Atsu is 9; Agyappng is 27.