Question

A mandatory competency test for second-year high school students has a normal distribution with a mean of 485 and a standard deviation of 85. a) The top 2% of students receive $500. What is the minimum score you would need to receive this award? b) The bottom 4% of students must go to summer school. What is the minimum score you would need to stay out of this group?

Answer 1

Solution:-

Given that,

mean = = 485

standard deviation = = 85

a) Using standard normal table,

P(Z > z) = 2%

= 1 - P(Z < z) = 0.02  

= P(Z < z) = 1 - 0.02

= P(Z < z ) = 0.98

= P(Z < 2.05 ) = 0.98  

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 85 + 485

x = 659.25

x = 659

b) Using standard normal table,

P(Z < z) = 4%

= P(Z < z ) = 0.04

= P(Z < -1.75 ) = 0.04  

z = -1.75

Using z-score formula,

x = z * +

x = -1.75 * 85 + 485

x = 336.25

x = 336