Question

The breaking strength of a rivet has a mean value of 10000 psi and a standard deviation of 500 psi. What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9900 and 10200?

Answer 1

Concepts and reason

A standard normal distribution is a normal distribution with mean and standard deviation $o=1. $ A Z-score indicates how many standard deviations an element is from the mean. And a Z-score is a numerical measurement of a value’s relationship to the mean in a group of values. Z-scores may also be positive or negative.

The positive value indicates that the score is above the mean.

The negative value indicates that the score is below the mean.

Fundamentals

The probabilities for the standard normal distribution are given in table of areas under the normal distribution or using the Excel function $(=NORM.S.DIST(2,TRUE)) $

The table gives the probabilities of the form

The mean and standard deviation of the breaking strength of a rivet are and.

Let X denotes mean breaking strength. .

For a random sample of 40 rivets, the mean and standard deviation are,

Then,

The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9900 and 10200 is,

Ans:

The probability that the sample mean is between 9900 and 10200 is 0.8905.