Question

The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4. What is the probability the sample mean score of 64 randomly selected students is between 74 and 76?

Answer 1

Solution :

Given that,

mean = = 75

standard deviation = = 4

n=64

= 75

=  / n = 4 / 64=0.5

= P(74<    <76 ) = P[(74 - 75) /0.5 < ( - ) / < (76 - 75) / 0.5)]

= P(-2 < Z <2 )

= P(Z <2 ) - P(Z <-2 )

Using z table,  

= 0.9772 -0.0228

= 0.9544