Question

Suppose that the amount of time that Parsnip takes to eat his food follows an approximate normal distribution with mean 41.25 seconds and standard deviation 4.4 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 X with bar on top, the resulting mean amount of time that Parsnip takes to eat his food for this sample of 20 days.

Answer 1

solution:

Given that ,

mean = = 41.25

standard deviation = = 4.4

n = 20

sampling distribution of X

sample distribution of sample mean is ,

=

= 41.25

sampling distribution of standard deviation

=  / n = 4.4/ 20

= 0.9839 (standard error)