Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 136 millimeters, and a variance of 36. If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.9 millimeters

Answers

Answer 1

Answer:

0.025 = 2.5% probability that the sample mean would differ from the population mean by greater than 1.9 millimeters

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 136 millimeters, and a variance of 36.

This means that [tex]\mu = 136, \sigma = \sqrt{36} = 6[/tex]

Sample of 50:

This means that [tex]n = 50, s = \frac{6}{\sqrt{50}} = 0.8485[/tex]

What is the probability that the sample mean would differ from the population mean by greater than 1.9 millimeters?

This is the probability that it is less than 136 - 1.9 = 134.1 millimeters or more than 136 + 1.9 = 137.9 millimeters. Since the normal distribution is symmetric, there probabilities are equal, which means that we can find one of them and multiply by two.

Probability that it is less than 134.1 millimeters:

This is the pvalue of Z when X = 134.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{134.1 - 136}{0.8485}[/tex]

[tex]Z = -2.24[/tex]

[tex]Z = -2.24[/tex] has a pvalue of 0.0125

2*0.0125 = 0.025

0.025 = 2.5% probability that the sample mean would differ from the population mean by greater than 1.9 millimeters


Related Questions


The graph of f (x) = (x - 2)² + 1 is shown below. What would the new equation of the function be if it is shifted up 2 units?

Answers

Answer:

f (x) = (x - 2)² + 3

Step-by-step explanation:

Adding 2 to the constant k would shift the entire equation upwards by 2.

-6x+8y=12 and -3x+4y=6

Answers

Answer:

3441

Step-by-step explanation:

PLS HOPE THIS HELP

Help asap
Find the value of x. Round to the
nearest tenth.
3
4
X =
= [?]

Answers

Answer:

36.9°

Step-by-step explanation:

→ Identify the triangle required by seeing which side is not given

Hypotenuse is not given so we need to use Tan⁻¹ = Opposite / Adjacent

→ Substitute values in

Tan⁻¹ =  ( 3 ÷ 4 )

→ Simplify

36.9°

17. An equation is shown.
3x7=+7
What number makes the number sentence true?
A 3
B, 14
C. 21
D. 28

Answers

the answer is 1 because 1x7=+7

What is the y-intercept for this function?
y = x2 - 2x - 3

Answers

Answer:

-3

Step-by-step explanation:

Need the answer for x and y

Answers

Answer:

x = 7°

y = 10°

Step-by-step explanation:

7x = 49

x = 7°

180 = 13y + 1 + 49

combine like terms:

13y = 130

y = 10°

Answer:

X equals to 7 & y equals to 10 'cause ;

7X=49

X=7

50 + 13 y + 1 = 180

13y = 130

y=10

Step-by-step explanation:

Good luck.

hope it was helpful for u .

5, 4, 16/5 find the 7th term

Answers

Answer:

a₇ = [tex] \frac{4096}{3125} [/tex]

5. A company intends to collect a random sample of size n from a population
with population proportion of interest p. Which of the following situations would
result in the smallest standard deviation of the sampling distribution of p?

Answers

Answer:D

Step-by-step explanation:

The situations that would result in the smallest standard deviation of p is; The population proportion p ≠ 0.5, and the sample size is n.

What is the standard deviation?

The formula for the standard deviation here is;

SD = √(n(p(1 - p))

Now, for the standard deviation to be maximum, it means that p = 0.5 and as such 1 - p will also be 0.5.

However, for Standard deviation to be smallest, then it means that p ≠ 0.5.

Secondly, for the sample size, it will have to remain as n and not 2n because when we say 2n, we are increasing the sample size which will in turn increase the standard deviation.

Read more about standard deviation at;

PLEASE HELP!!!!!!!!!! BRAINLIEST
Add the following fractions. Simplify and reduce to the lowest terms.

9/16 + 3/16

Answers

Answer:

3/4

Step-by-step explanation:

12/16

divided by 4

3/4

Answer: /34

Step-by-step explanation:

 9/16 + 3/16

=(9+3)/16 ⇔ Fractions with the same denominator can subtract or add

=12/16 ⇔ Simplify

=(3×4)/(4×4) ⇔ Factor each number

=3/4 ⇔ Divide 4 on both numerator and denominator

Hope this helps!! :)

Please let me know if you have any questions

Find the surface area of the rectangular prism (above) using its net (below).

Correct answer will receive a cookie and branilist

Answers

Answer:

62

Step-by-step explanation:

15+15+10+10+6+6= 62

WILL MARK BRAINLYEST


A street sign is 8 feet tall and casts a shadow that is 28 feet long. At the same time, a nearby tree casts a shadow that is 210 feet long. How tall is the tree?

A.60
B.70
C.80
D.90

Answers

The answer is 60



Explanation: The shadows are 3.5 times bigger than the original height so you divide 210 by 3.5 and you get 60. I hope this helped.

Apr 08, 12:51:17 AM
Brittney wants to buy grapes and apples to bring to a party. Grapes cost $1.60
per pound and apples cost $1.75 per pound. If she only has $10 to spend on
grapes and apples, which inequality represents the situation where she buys x
pounds of grapes and y pounds of apples?
1.60x + 1.75y < 10
1.60x + 1.75y > 10
Submit Answer
1.75x + 1.60y < 10
1.75% + 1.60y > 10
Type here to search
O
12:5
4/8/

Answers

Answer: did you get a answer yet?

Step-by-step explanation:

6(5 - 8n) + 12 = -54
please step my step

Answers

Answer:

Look Below

Step-by-step explanation:

6(5 - 8N) + 12 = -54

-48N + 30 + 12 = -54

-48N + 42 = -54

(-48N + 42) + (-42) = -54 + (-42)

-48N = -96

-48N / 48 = N

-96 / 48 = 2

N = 2

Hope This Helps! If you find any fault in my answer please let me know. Thanks! Have a good day!

help plese i beg of you

Answers

9514 1404 393

Answer:

k = 45 . . . miles per hourk = 1/45 . . . hours per mile

Step-by-step explanation:

One way we can relate distance and time is ...

  time = k × distance

Then the value of k (the constant of proportionality) is ...

  k = time/distance = 4 hours/(180 miles)

  k = (1/45) hours/mile

__

Another way we can relate the variables is ...

  distance = k × time

Then the value of k (the constant of proportionality) is ...

  k = distance/time = (180 miles)/(4 hours)

  k = 45 miles/hour

Approximately how long will it take a jet to travel 400 miles at a rate of 120
miles per hour?
A.) 3 1/3
B.)3 1/2
C.)4 1/2
D.)4 1/3

Answers

Answer:

3  1/3

Step-by-step explanation:

What is the value of C in the matrix equation below?
|-18 3 51-c-[-22 1 12
o -40
217]
01-40 27]
10142-7)
0 14 2 17]

Answers

Given:

The matrix equation is:

[tex]\begin{bmatrix}-18&3&5\end{bmatrix}-C=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]

To find:

The value of matrix C.

Solution:

Let [tex]A=\begin{bmatrix}-18&3&5\end{bmatrix},B=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]. Then the given equation can be rewritten as

[tex]A-C=B[/tex]

[tex]-C=B-A[/tex]

[tex]C=-(B-A)[/tex]

[tex]C=A-B[/tex]

On substituting the values of the matrices, we get

[tex]C=\begin{bmatrix}-18&3&5\end{bmatrix}-\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]

[tex]C=\begin{bmatrix}-18-(-22)&3-1&5-12\end{bmatrix}[/tex]

[tex]C=\begin{bmatrix}-18+22&2&-7\end{bmatrix}[/tex]

[tex]C=\begin{bmatrix}-4&2&-7\end{bmatrix}[/tex]

Therefore, the correct option is C.

Answer: C

Step-by-step explanation: [ 4 2 -7 ]

Find the slope of the line that passes through the given points.

Answers

Answer: -1/6

Step-by-step explanation:

slope= change of y over change of x

3-4/ 5--1=

-1/6

Hope this helps!

Answer:

-1/6

Step-by-step explanation:

(-1, 4) and (5, 3)

y2 - y1 / x2 - x1

y2 = 3

y1 = 4

x2 = 5

x1 = -1

(3 - 4) / (5 - -1)

-1 / 6

slope = -1/6

please help me
A book is marked 21% off. If the original price is $23.42, what will the sale price be?

Round your answer to the nearest cent. Do not include units with your answer.

Answers

Answer:

$18.51

Step-by-step explanation:

23.42×.21= 4.91 then 23.42-4.91= your sale price which is $18.51

Hakima and Joshua both opened savings accounts. Both started with a balance of zero dollars. For every $3 that Hakima saves in her account, Joshua saves $5. If they have saved a total of $336, how much did Hakima save?

Answers

I’m pretty sure that would be $112

ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY ​​IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE ​​​

Answers

Answer:

It is 47.5 or 47 1/2

Step-by-step explanation:

The formula for volume of a prism is base x height.

The base is the area of the rectangle at the bottom. The area of a rectangle is, of course, length times width, so 2.5 x 4=10.

So, the base is 10.

Now, the second part of the formula is height.

The height is 4.75.

Now, do the formula: Base x height : 10 x4.75

The answer is 47.5.

Don't report me lol. I promise it is correct.

Answer:

I need 5 Brainliest before I can become Ace

Step-by-step explanation:

The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.
The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.

Answers

Answer:

The quadratic equation y = -4x2 + 80x - 150 models the store's daily profit, y, for selling footballs at x dollars. you can subtract 150 from both sides and use the quadratic formula to find x=4. It can make at most 120 units in one day. 3 1. Backward Bending Supply Curve.

Plz help NO LINKS this is due today

Answers

Answer:

It is C, the metric system

The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?

Answers

9514 1404 393

Answer:

  12 ft

Step-by-step explanation:

Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...

  A = LW

  264 = (2w-2)w

  132 = w² -w . . . . . . . divide by 2, eliminate parentheses

  132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square

  √132.25 = w -0.5 . . . . . take the square root

  0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root

The width of the living room is 12 feet.

90:(3+6)-20.(60-55) propiedad

Answers

Answer:

https://www.commoncoresheets.com/Math/Properties/Applying%20Properties%20of%20Operations/Spanish/2.pdf

Step-by-step explanation:

This will help you:) not a spam link its a pdf that brings you straight to the worksheet <3

A minute- hand of a clock is 16 in long. Find the distance traveled by the tip of the minute - hand in one hour.

Answers

Answer: 16/2=8
8 * 8 = 64
64* 3.14 = 200.96
200.96 * 60 = 12057.6

Hope this helps (:

Find the dot product of vectors u = -4i + 7j and v = 2i + j

Answers

Answer:

The desired dot product is -1

Step-by-step explanation:

To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:

dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1

The desired dot product is -1

Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3

Answers

Answer:

[tex]\dfrac{-8}{x+3}[/tex]

Step-by-step explanation:

We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".

Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.

So, we can write it as follows :

[tex]\dfrac{-8}{x+3}[/tex]

Hence, this is the required solution.

HELP PLEASEEEE!!! SOMEONE HELP ME FOR ONCE, NO ONE IS ANSWERING MY QUESTIONS AND IM SO FREAKING STRESSED OUT. OH MY GOD SOMEONE PLS IM BEGGING YOU EXPLAIN YOUR ANSWER STEP BY STEP FOR ONCE

In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
a) 112,000 members
b) 78,000 members
c) 151,000 members
d) 127,000 members

Answers

Answer:

I have come to the conclusion that it is A. 112,000

Answer:

d) 127,000 members

Step-by-step explanation:

In this problem we have an exponential function of the form

where  a is the initial value

b is the base

The base is equal to  b=1+r

r is the average rate

In this problem we have  a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

Round to the nearest thousand

What does MIJ equal ?

Answers

What that guy is typing

Round 12,628 to nearest 1,000

Answers

Answer:

13000

Step-by-step explanation:

it's closer to 13000 than to 12000

Answer:

13000

Step-by-step explanation:

12628 >>>13000

Me:

This is easy like what grade are you in?

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