Question

Assume that test scores in a course are normally distributed with a mean of 62 and a standard deviation of 12. In a class of 2,000 people, approximately how many students would have scored

a. above 74?

b. between 38 and 86?

c. below 38?

PLEASE SHOW WORK

Answer 1

Solution :

Given that ,

a) P(x > 74) = 1 - p( x< 74)

=1- p P[(x - ) / < (74 - 62) / 12]

=1- P(z < 1)

= 1 - 0.8413

= 0.1587

b) P( 38 < x < 86 ) = P[(38 - 62) / 12) < (x - ) /  < (86 - 62) / 12) ]

= P(- 2 < z < 2)

= P(z < 2 ) - P(z < - 2)

Using z table,

= 0.9772 - 0.0228

= 0.9544

c) P(x < 38)

= P[(x - ) / < (38 - 62) / 12]

= P(z < - 2 )

Using z table,

= 0.0228