Question

According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.06 inches. What is the probability that the mean daily precipitation will be 0.11 inches or less for a random sample of 40 November days (taken over many years)?

Answer 1

Solution:

Given: the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.06 inches.

thus and

Sample size = n = 40

We have to find:

P( the mean daily precipitation will be 0.11 inches or less ) =..........?

Since sample size n = 40 is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Thus find z score for

Thus we get:

Look in z table for z = 1.0 and 0.05 and find corresponding area.

P( Z< 1.05 ) = 0.8531

Thus