PLEASE HELP ! (4/5) - 50 POINTS -

Answer:

A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. β  = 0.0122

C. β  = 0.0000

Step-by-step explanation:

Given that:

Mean = 100

standard deviation = 2

sample size = 9

The null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 100}[/tex]

[tex]\mathtt{H_1: \mu \neq 100}[/tex]

A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .

Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]

∴

[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]

[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]

when  [tex]\mu = 100[/tex]

[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]

[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]

From the standard normal distribution tables

[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]

[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]

[tex]\mathbf{\alpha = 0.0244 }[/tex]

Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. Find beta for the case where the true mean heat evolved is 103.

The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]

Thus;

β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )

∴

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 103[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]

[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]

From standard normal distribution table

β  = 0.0122 - 0.0000

β  = 0.0122

C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 105[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]

[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]

From standard normal distribution table

β  = 0.0000 - 0.0000

β  = 0.0000

The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.

Answer:

38%

Step-by-step explanation:

First determine her savings

560-347.49

212.51

Then divide by the total amount

212.51/560

.379482143

Change to percent form

37.948%

Answer:

38%

Step-by-step explanation:

[tex]560.00-347.49=212.51\\212.51\div560.00==38[/tex]

Answer:

x=7

Step-by-step explanation:

If P is the midpoint of XY, then XP = PY:

9514 1404 393

Answer:

  3. 151°

  4. 42°

Step-by-step explanation:

3. The measure of the supplement is found by subtracting the angle from 180°.

  supplement of 29° = 180° -29° = 151°

__

4. The total of angles in a triangle is 180°, so the third one can be found by subtracting the other two from 180°.

  third angle = 180° -128° -10° = 42°

Answer:

I canot answer this

Step-by-step explanation:

Answer:

Lower quartile= 4.75

Middle quartile= 9.5

Upper quartile= 14.25

Step-by-step explanation:

The given date set is 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

On counting them we notice that it's number of element is 18

So N = 18

Arranging them in ascending order gives

12,18,18,20,23,24,24,25,25,29,31,43,43,43,53,53,65,78

Lower quartile= (N+1)*1/4

Lower quartile= (18+1)/4

Lower quartile= 19/4

Lower quartile= 4.75

Middle quartile= (N+1)*2/4

Middle quartile= (18+1)*2/4

Middle quartile= (19)*2/4

Middle quartile= 9.5

Upper quartile= (N+1)*3/4

Upper quartile= (18+1)*3/4

Upper quartile= (19)*3/4

Upper quartile= 14.25

Inter quartile range = upper quartile- minutes lower quartile

= 14.25-4.75

= 9.5

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]

                                                                  = 4.42

So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5)    {using continuity correction}

        P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5)   {using continuity correction}

       P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852

       P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.

Answer:

D = 240 - 30t

Step-by-step explanation:

If the equation represents her distance from City A, we need to include 240 in the equation to represent the distance to the city.

Then, we need to subtract 30t from 240 in the equation because 30t represents how far she will have traveled in t hours.

So, D = 240 - 30t is the equation that will represent Layla's distance from the city.

for x ,

8x + 10x = 180°

[sum of linear pair is equal to 180°]

or, 18x = 180°

or, x = 180/18

therefore, x = 10°……

for z,

10z =8x

[ being corresponding angles are equal ]

or, 10z = 8 × 10°

( replacing x by 10°)

or, 10z = 80°

or, z = 80/10

thus z = 8°…………

Answer:

[tex]\boxed{x=1}[/tex] and [tex]\boxed{x=7}[/tex]

Step-by-step explanation:

This quadratic is already factored down to its factors (x - 1) and (x - 7).

Set these equal to zero and solve for x by adding 1 or 7 to both sides of the equation.

[tex]x-1=0\\\\\boxed{x=1}[/tex]

[tex]x-7=0\\\\\boxed{x=7}[/tex]

Answer:

D

Step-by-step explanation:

-0.81 is a high negative correlation, which means the y is decreasing with x increasing, which means y(the number of broken glass) decreases when x(amount of paper used) increased. So we can say that the toilet paper is surely helping.

make me brainly if you find it correct

Answer:

f(g(1)) = - 2

Step-by-step explanation:

Find g(1) then use the value obtained to find f(x)

g(1) = 1 ← value of y when x = 1 (1, 1 ) , then

f(1) = - 2 ← value of y when x = 1 (1, - 2 )

Answer:

2x-3

Step-by-step explanation:

f(x) = 3x-1

g(x)= x+2

(f-g) (x) = 3x-1 - (x+2)

Distribute the minus sign

             = 3x-1 -x-2

 Combine like terms

               = 3x-x -1-2

                =2x -3

Answer:

139 cards

Step-by-step explanation:

This is basically just a division statement - we have 417 cards and want to split it with 3 people (two friends + himself = 3 people).

We can divide these using a calculator or long division, but either way you will get:

[tex]417\div3=139[/tex]

Hope this helped!

Answer: 139

Step-by-step explanation:

417 divided by 3 gives you 139.

Answer:

92.9997<[tex]\mu[/tex]<99.5203

Step-by-step explanation:

Using the formula for calculating the confidence interval expressed as:

CI = xbar ± Z * S/√n where;

xbar is the sample mean

Z is the z-score at 90% confidence interval

S is the sample standard deviation

n is the sample size

Given parameters

xbar = 96.52

Z at 90% CI = 1.645

S = 10.70.

n = 25

Required

90% confidence interval for the population mean using the sample data.

Substituting the given parameters into the formula, we will have;

CI = 96.52 ± (1.645 * 10.70/√25)

CI = 96.52 ± (1.645 * 10.70/5)

CI = 96.52 ± (1.645 * 2.14)

CI = 96.52 ± (3.5203)

CI = (96.52-3.5203, 96.52+3.5203)

CI = (92.9997, 99.5203)

Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203

ans: 257,256.59

if it was sold for $3.99

it would have been 86,047 × $3.99 = 343,303.59 and it was sold for $1 instead so automatically it's $86,047

therefore

343, 303.59

-86, 047 which is equal to a loss of $257, 256.59

Answer:

y = 15°

Step-by-step explanation:

Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:

5y + 5y + 2y = 180

12y = 180

y = 15°

The equation of the straight line is [tex]x+y=2[/tex].

Given:

To find: The equation of this line

It is given that a line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex]

Now, it is given that the referred line has intercepts (a, 0) and (0, a). Then, using the above statement, the equation of this line can be written as,

[tex]\frac{x}{a} +\frac{y}{a}=1[/tex]. It is already given that [tex]a\neq 0[/tex]. So, we need not mention it again.

It is also given that the point (-2, 4) lies on this line. Then, the coordinates of this point must satisfy the equation of the line.

This implies that,

[tex]\frac{-2}{a} +\frac{4}{a} =1[/tex]

[tex]\frac{2}{a} =1[/tex]

[tex]a=2[/tex]

Now, put [tex]a=2[/tex] in the equation of the line, [tex]\frac{x}{a} +\frac{y}{a}=1[/tex] to get,

[tex]\frac{x}{2} +\frac{y}{2} =1[/tex]

[tex]x+y=2[/tex]

So, the equation of the line is [tex]x+y=2[/tex].

Learn more about equations of straight lines here:

https://brainly.com/question/18879008

Answer:

Step-by-step explanation:

3w + 2c = 32

4w + 3c = 44

Multiply the 1st equation by 4 and 2nd equation by 3, we get:

12w + 8 c = 128

12w + 9 c = 132

Subtracting the top equation from the bottom equation, we get: c = 4

Substituting c = 4 in any one of the above equations and solving, we get: w = 8

Therefore, weight of 2w + 1c = 2(8) + 4 = 20 pounds (Answer)

Step-by-step explanation:

X +1 + X + 2

X + X + 1 + 2

2x + 3

Therefore it's 2x + 3

Answer:

-10

Step-by-step explanation:

We can substitute c into the equation as -2.

[tex]-(-2) - 12[/tex]

Two negatives make a positive:

[tex]2-12[/tex]

And [tex]2 - 12 = -10[/tex].

Hope this helped!

Answer:

They can go on 14 rides the maximum.

Step-by-step explanation:

First, you have to set up the equation. Basically, Aiko and Kendra only carry $60 with them. They cannot go over that limit. Furthermore, the entrance free is $17. Each ride is $3.

(x = the amount of rides)

17 + 3x ≤ 60

17 represents the entrance fee which only has to be paid one time. 3x represents the cost of each ride (x equals to the amount of rides).

Now you solve.

Isolate the variable, which is 3x.

3x ≤ 60 - 17

3x ≤ 43

Now, divide 43 by 3 to find the value of x.

x ≤ 43 ÷ 3

x ≤ 14.3333333333

They can go on a max of 14 rides. Anymore, and they will go over budget. Normally, with problems like this one, if you have a decimal, you should round down unless your instructor says otherwise.

After all, who would you be able to go on a third of a ride? It isn't possible, so generally, they just have you round down.

Answer:

KI and HE are parallel

So we apply the law of exterior angles ;

3X=X + 180– 2X

3X +X = 180

4X= 180

X= 180/4

X= 45

I hope I helped you^_^

Answer: [tex]A=6000(1.012)^t[/tex]

Step-by-step explanation:

General exponential function:

[tex]A=P(1+r)^t[/tex]

, where P= current  population

r= rate of growth

t= time period

A= population after t years

As per given , we have P=6,000

r= 1.2% = 0.012

Then, the required exponential function:  [tex]A=6000(1+0.012)^t[/tex]

or [tex]A=6000(1.012)^t[/tex]

Answer:

Ashley= 15

Milan= 11

Carlos= 105

Step-by-step explanation:

Let, A, M and C denotes Ashley, Milan and Carlos respectively.

A+M+C= 131 (according to the question)

Here,

C= 7A

A= M+ 4

So, M= A - 4

Now,

A+M+C = 131

or, A+ A-4+ 7A = 131 (putting the values)

or, 9A - 4 = 131 (adding like terms i.e. A + A + 7A)

or, 9A = 131 + 4

or, 9A = 135

or, A = 135 / 9

So, A = 15

C= 7A = 7×15= 105

M= A-4 = 15 - 4 = 11

Answer:

1/2 mi

Step-by-step explanation:

Fairfax to Greenwood is equal to one mile

Now think of it as an equation and substitute 1/2 for fairfax and x for greenwood

1/2 + x = 1

This means that x = 1/2

Because of this from Arcadia to Greenwood it is 1/2 mi