1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DanielleElmas [232]
2 years ago
7

A company makes windows for use in homes and commercial buildings. The standards for glass thickness call for the glass to avera

ge 0.325 inch with a standard deviation equal to 0.065 inch. Suppose a random sample of n = 44 windows yields a sample mean of 0.337 inch.
Required:
What is the probability of x >= 20.337 if the windows meet the standards?
Mathematics
1 answer:
Hatshy [7]2 years ago
8 0

Answer:

0.1102 = 11.02% probability of x >= 0.337 if the windows meet the standards.

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

The standards for glass thickness call for the glass to average 0.325 inch with a standard deviation equal to 0.065 inch.

This means \mu = 0.325, \sigma = 0.065

Sample of 44

This means that n = 44, s = \frac{0.065}{\sqrt{44}}

What is the probability of x >= 0.337 if the windows meet the standards?

This is 1 subtracted by the p-value of Z when X = 0.337. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.337 - 0.325}{\frac{0.065}{\sqrt{44}}}

Z = 1.225

Z = 1.225 has a p-value of 0.8898

1 - 0.8898 = 0.1102

0.1102 = 11.02% probability of x >= 0.337 if the windows meet the standards.

You might be interested in
The ratio of collectible coins Juanita owns to coins that Elia owns is 3:1. Elia has 32 coins. How will the ratio of Juanita’s c
yaroslaw [1]
Hi there Maebe, since the ratio is 3:1 your answer is 96.

The ratio 3:1 is just saying Juanita has 3 times whatever Elita has. So, Elita’s 32 times 3 equals 96. :) I hope I’ve helped you. Please give me feedback if you need more help understanding!
7 0
2 years ago
A fence around a rock garden is the shape of a right triangle.two angles measure 30 and 60 degrees.two sides measure 10 feet and
sveticcg [70]
All you gotta do is add up the two sides and then subtract it from 47.3 .
So 10+17.3= 27.3
47.3-27.3= 20
7 0
2 years ago
Rosa has 3 3/4 pounds of dough. She uses 1/8 of a pound for one roll. How many rolls could be made from Rosa's dough?
Vlada [557]
3 3/4 pounds so 3×3/4 = 2 1/4(mixed fraction)
2 1/4÷ 1/8= 2 1/4 × 8/1
for fraction division, yo
u keep the first fraction and flip the second fraction around. than you change the divide sign to multiply sign to find the answer
5 0
2 years ago
How many edges does a rectangle prism have?
creativ13 [48]

the answer to your question there would be 12

4 0
3 years ago
Read 2 more answers
5x - (x + 3)= 1/3 (9x + 18) - 5
telo118 [61]
1/3(9x) =3x
1/3(18) =6

3x+6-5

Then you do
-(x)=-x
-(3)=-3

5x-x-3 = 4x-3

4x-3=3x+6-5
4x-3=3x+1

x=4
4 0
2 years ago
Read 2 more answers
Other questions:
  • One week, Claire earned $272.00 at her job when she worked for 17 hours. If she is paid the same hourly wage, how many hours wou
    11·2 answers
  • What is a line segment
    13·1 answer
  • LAST ONE!! (:
    8·1 answer
  • Suppose y = f (x) +k what effect does k have on parent funcation
    9·1 answer
  • Antonia is using the calculator shown to find the value of
    15·2 answers
  • 5.
    8·1 answer
  • Ryan has three consecutive scores for math. The sum of these scores is
    8·1 answer
  • Select all the TRUE sentences!!!
    9·2 answers
  • A function f(x) = x^2 - 4 has a domain as the set of integers
    6·1 answer
  • Xzavier has a meal in a restaurant. He adds up the prices listed on the menu for everything they ordered and gets a subtotal of
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!