Question

Use the z-score table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

A psychologist finds that the intelligence quotients of a group of patients are normally distributed, with a mean of 99 and a standard deviation of 16. Find the percent of the patients with the following IQs.

(a) above 111

(b) between 87 and 117

Answer 1

solution

P(x >111 ) = 1 - P(x<111 )

= 1 - P[(x - ) / < (111-99) /16 ]

= 1 - P(z <0.75 )

Using z table

= 1 - 0.7734

= 0.2266

answer=22.66%

(B)

P(87< x <117 ) = P[(87-99) /16 < (x - ) / < (117-99) /16 )]

= P( -0.75< Z <1.125 )

= P(Z <1.125 ) - P(Z <-0.75 )

Using z table   

= 0.8697-0.2266

answer= 64.31%