Question

1.             Suppose the age of the customers at post office has a non-normal distribution with mean 40 and standard deviation 5 years.

i.     Select 100 customers at random. What is the distribution of their average age? Describe its shape, it’s mean, and standard error.

ii.   What is the chance that the average age for 100 customers from the post office is over 41?

iii.  Would you take the same approach to the previous two parts if you had a sample of only 2 customers?

Answer 1

Solution:

Given: Suppose the age of the customers at post office has a non-normal distribution with mean 40 and standard deviation 5 years.

That is: Mean = and Standard Deviation =

Part i) n = 100

What is the distribution of their average age? Describe its shape, it’s mean, and standard error.

Since sample size = n = 100 is large sample size , the distribution of their average age is approximately Normal distribution with

Mean of sample means = and standard deviation of sample mean, that is standard error is:

Part ii) What is the chance that the average age for 100 customers from the post office is over 41?

That is:

Find z score

Thus we get:

Look in z table for z = 2.0 and 0.00 and find area, which gives: P( Z< 2.00) = 0.9772

Thus

Part iii) Would you take the same approach to the previous two parts if you had a sample of only 2 customers?

No, since sample size = n = 2 is very small sample size and hence we can not use Normal or approximate Normal distribution approach.