Question

I need explanation for this problem:

The breaking strength of a certain type of fabric has mean 1.86 and standard deviation .2. A random sample of 49 pieces of fabric is drawn.

A- What is the probability that the sample mean breaking strength is less than 1.8?

B- How large a sample size is needed so that the probability is .06 that the sample mean is less than 1.8?

Ans for (A)= 0.02

Ans for (B)= 27

Answer 1

Answer(A):

Given that,

We need to calculate

To calculate this, let us first standardize the .

Let be the standardized value of and is given by,

substituting the given values, we get

Then from standard normal distribution table (Z table),

(two decimal places)

Answer (B):

Here given that, .

We need to calculate . Again from Z table (Or in MS Excel type =NORMINV(0.06))

Then again using the above mentioned formula for , we get

substituting the given values, we get