The mean score in the past years of an employee evaluation e

The mean score in the past years of an employee evaluation exam was 68 with a standard deviation of 12. What percent scored between 60 and 85? What percent scored 90 or higher?

Solution

The mean score in the past years of an employee evaluation exam was 68 with a standard deviation of 12. What percent scored between 60 and 85? What percent scored 90 or higher?

Z value for 60, z=(60-68)/12 = -0.67

Z value for 85, z=(85-68)/12 = 1.42

P( 60<x<85) = P( -0.67<z<1.42)

=P( z <1.42)-P(z <-0.67)

= 0.9222 - 0.2514

=0.6708

percent scored between 60 and 85 = 67.08%

Z value for 90, z=(90-68)/12 = 1.83

P( x >90) = P( z >1.83)

= 0.0336

percent scored 90 or higher = 3.36%