Question

A random sample of size 40 is taken from a population with mean µ = 240 and standard deviation σ = 26.

i. Describe the probability distribution of the sample mean.

ii. What are the mean and the standard deviation of the sample mean?

iii. Calculate the probability that the sample mean is between 230 and 250.

Answer 1

Solution :

Given that ,

mean = = 240

standard deviation = =26

n = 40

sample distribution of sample mean is ,

=

= 240

sampling distribution of standard deviation

=  / n = 26/ 40

= 4.11

P(230<     < 250) = P[(230-240) /4.11 < ( - ) /   < (250-240) /4.11 )]

= P( -2.43< Z <2.43 )

= P(Z <2.43 ) - P(Z <-2.43 )

Using z table

=0.9925 - 0.0075

=0.9850

probability= 0.9850