Mathematics, 18.07.2021 22:30 girl88

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is normally distributed.

Answers: 3

Show answers

Answers

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

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 average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.

This means that $\mu = 2000, \sigma = 100$

A sample of 20 cables is selected and tested.

This means that $n = 20, s = \frac{100}{\sqrt{20}} = 22.361$

Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.

This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So

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

By the Central Limit Theorem

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

$-1.645 = \frac{X - 2000}{22.361}$

X - 2000 = -1.645*22.361

X = 1963.2

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Answer from: Quest

900 degrees

step-by-step explanation:

Answer from: Quest

c) yes, because of asa or aas

Another question on Mathematics

Mathematics, 21.06.2019 13:40

Acertain standardized? test's math scores have a? bell-shaped distribution with a mean of 520 and a standard deviation of 105. complete parts? (a) through? (c)

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

17 in long 1.3 ft wide and 8in high what is the volume

Answers: 1

Answer

Mathematics, 21.06.2019 20:20

One of every 20 customers reports poor customer service on your company’s customer satisfaction survey. you have just created a new process that should cut the number of poor customer service complaints in half. what percentage of customers would you expect to report poor service after this process is implemented? 1.) 5% 2.) 10% 3.) 2% 4.) 2.5%

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 25002500 grams and a standard deviation of 800800 grams while babies born after a gestation period of 40 weeks have a mean weight of 27002700 grams and a standard deviation of 385385 grams. if a 3232-week gestation period baby weighs 21252125 grams and a 4040-week gestation period baby weighs 23252325 grams, find the corresponding z-scores. which baby weighs lessless relative to the gestation period?

Answers: 1

Answer

You know the right answer?

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard devi...

Questions

Mathematics, 10.12.2020 01:10

The following system of linear equations is solved by graphing them on the coordinate plane. y=3x−2y=−3/5x−1 Which ordered pair is the be...