Question

c. A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. The top 3% receive $500. What is the minimum score you would need to receive this award ?

Answer 1

Solution:-

Given that,

mean = $\mu$ = 400

standard deviation = $\sigma$ = 100

Using standard normal table,

P(Z > z) = 3%

= 1 - P(Z < z) = 0.03  

= P(Z < z) = 1 - 0.03

= P(Z < z ) = 0.97

= P(Z < 1.881 ) = 0.97  

z = 1.881

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.881 * 100 + 400

x = 588.1

minimum score = 588