Question

A random sample of 64 observations is to be been drawn from a distribution with mean
15 and standard deviation 10. Find the probability that the sample mean, x̅ , will differ
from μ by no more than 2 units in either direction. Interpret your results.

Answer 1

Solution :

Given that ,

mean = = 15

standard deviation = = 10

n = 64

=   = 15

= / n = 10/ 64 = 1.25

15 ± 2 = 13, 17

P(13 < < 17)  

= 1 - P[(13 -15) / 1.25 < ( - ) / < (17 - 15) / 1.25)]

= 1 - P( -1.60 < Z < 1.60 )

= 1 - P(Z < 1.60) - P(Z < -1.60)

Using z table,  

= 1 - P( 0.9452 - 0.0548)   

= 1 - 0.8904

= 0.1096

The probability that a 64 randomly selected will differ from μ by no more than 2 units in either direction  is 0.1175