Question

The scores on a standardized test have an average of 1200 with a standard deviation of 60. A sample of 50 scores is selected.

What is the probability that the sample mean will be between 1195 and 1205? Round your answer to three decimal places.

Answer 1

Solution :

Given that ,

mean = = 1200

standard deviation = = 60

n = 50

= 1200

=  / n = 60/ 50=8.485

P(1195<   <1205 ) = P[(1195-1200) / 8.485< ( - ) /   < (1205-1200) / 8.485)]

= P(-0.59 < Z <0.59 )

= P(Z <0.59 ) - P(Z <-0.59 )

Using z table,  

= 0.7224-0.2776

=0.4448