Question

A test has a mean of 81 and a Standard Deviation of 8.  What percentage of cases falls above a score of 77?   Below a score of 93?

Answer 1

Solution :

Given that,

mean = = 81

standard deviation = = 8

a ) P (x > 77 )

= 1 - P (x < 77 )

= 1 - P ( x -  / ) < (77 - 81 / 8 )

= 1 - P ( z <- 4 / 8 )

= 1 - P ( z < - 0.5 )

Using z table

= 1 - 0.3085

= 0.6915

Probability = 69.15%

b ) P( x < 93 )

P ( x - / ) < ( 93 - 81 / 8)

P ( z < 12 / 8 )

P ( z < 1.5 )

= 0.9332

Probability = 93.32%