Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16.7 inches, and standard deviation of 0.8 inches.

If 19 items are chosen at random, what is the probability that their mean length is less than 16.8 inches? Round your answer to 4 decimal places.

Answer 1

Given data

Population mean

Population standard deviation

No of samples taken (n) =19

And we have to find the probability of getting the mean of sample is less than 16.7

So sample mean

Now let's find the test statistics Z

So

Now from the standard probability distribution table for Z score we have probability value for Z=0.54 is

P=0.7054

As we see the bell shape curve we will find that this is the area left side to the 16.8 so it is the probability of getting the average length of the sample less than 16.8