Question

Suppose that the amount of time that Parsnip takes to eat his food follows an approximate normal distribution with mean 40.75 seconds and standard deviation 4.8 seconds. A simple random sample of 20 days is selected and the amount of time that Parsnip takes to eat his food is determined for each day. If appropriate, describe completely the sampling distribution of , the resulting mean amount of time that Parsnip takes to eat his food for this sample of 20 days.

Answer 1

Solution:

Given:  the amount of time that Parsnip takes to eat his food follows an approximate normal distribution with mean 40.75 seconds and standard deviation 4.8 seconds. thus and

Sample size = n = 20

We have to describe completely the sampling distribution of  the resulting mean amount of time that Parsnip takes to eat his food for this sample of 20 days.

Since  the amount of time that Parsnip takes to eat his food follows an approximate normal distribution, then sampling distribution of sample means also follows an approximate normal distribution with mean of sample means:

and standard deviation of sample means is: