Question

A population has a mean of 239 and a standard deviation of 128. If a sample of size 6 is taken, what is the probability the sample mean is less than 288.1? Enter your answer as a decimal to 3 decimal places.

A population has a mean of 474 and a standard deviation of 125. If a sample of size 8 is taken, what is the probability the sample mean is less than 536.4? Enter your answer as a decimal to 3 decimal places.

Answer 1

Given,

= 239 , = 128

Using central limit theorem,

P( < x) = P(Z < (x - ) / ( / sqrt(n) ) )  

a)

P( < 288.1) = P(Z < ( 288.1 - 239) / (128 / sqrt(6)) )

= P(Z < 0.94 )

= 0.826

b)

P( < 536.4) = P(Z < ( 536.4 - 474) / (125 / sqrt(8)) )

= P(Z < 1.41)

= 0.921