Question

Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.2. Round answers to the nearest tenth of a percent.

a) What percentage of scores will be less than 93? %
b) What percentage of scores will be more than 80? %
c) What percentage of scores will be between 79 and 88? %

Answer 1

Solution :

Given that,

mean = = 87

standard deviation = = 5.2

P(X<93 ) = P[(X- ) / < (93-87) /5.2 ]

= P(z <1.15 )

Using z table

= 0.8749

=87.49%

B.

P(X>80) =1 - P[(X- ) / < (80-87) /5.2 ]

=1 - P(z <-1.35 )

Using z table

=1-0.0885

=0.9115

=91.15%

C.

P( 79< Z <88 )

= P(Z < 88-87/5.2) - P(Z <79-87/5.2 )

Using z table   

= P(Z < 0.19) -P(Z<-1.54 )

=0.5753-0.0618

= 0.5135

=51.35%