Question

From a population which is according to a normal distribution with mean 10 units and standard deviation 8 units, a sample of size n=25 is taken. What would the distribution of the sum of the sample values be? Provide the name of the distribution and its parameters. Are any assumptions made regarding n?

Answer 1

solution:

Given that ,

mean = = 10

standard deviation = = 8

n = 25

this is the sampling distribution of the mean

=   =10.

sampling distribution of the standard deviation

= / n = 8 / 25 = 1.6

n is the random sample

it can accept central limit therom

n >30 population standard devitaion

n<30 sample standard deviation