Question

Q5. Given a normal population whose mean is 50 and whose standard deviation is 5, find the probabilities that the sample mean lies between 49 and 52 for the following sample sizes. a. = 4 b. = 16 c. = 25

Answer 1

a normal population has mean() is 50 and standard deviation() is 5

sampling distribution of mean:-

will follow normal distribution with:-

, n = sample size.

a). for n= 4,

will follow normal distribution with:-

the probabilities that the sample mean lies between 49 and 52 be:-

[ from standard normal table]

b). for n= 16,

will follow normal distribution with:-

the probabilities that the sample mean lies between 49 and 52 be:-

[ from standard normal table]

c). for n= 25,

will follow normal distribution with:-

the probabilities that the sample mean lies between 49 and 52 be:-

[ from standard normal table]

***in case of doubt, comment below. And if u liked the solution, please like.