Question

The mean per capita consumption of milk per year is 131 liters with a variance of 841.

If a sample of 132 people is randomly selected, what is the probability that the sample mean would be less than  133.5 liters? Round your answer to four decimal places.

Answer 1

Solution:
Given: The mean per capita consumption of milk per year is 131 liters with a variance of 841.

That is: and

then standard deviation =

Sample size = n = 132

Since sample size n = 132 > 30, we can assume large sample and hence we apply Central Limit theorem which states that for a large sample size , sampling distribution of sample means is approximately Normal with mean of sample means is and standard deviation of sample means is:

We have to find the probability that the sample mean would be less than  133.5 liters

That is:

Thus find z score:

Thus we get:

Look in z table for z =0.9 and 0.09 and find area.

P( Z< 0.99 ) = 0.8389

Thus

Thus the probability that the sample mean would be less than  133.5 liters is 0.8389