Question

Suppose SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 109. A university plans to award scholarships to students whose scores are in the top 2%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

Answer 1

Answer:

721.54

Step-by-step explanation:

We have to convert the 2% given in the statement into a z-score, as follows:

P (X> x) = 2% = 0.02, P (Z> z) = 0.02

thus find z such that:

P (Z <z) = 1 - P (Z> z)

P (Z <z) = 1 - 0.02

P (Z <z) = 0.98

we look for what value of z corresponds to in the normal distribution table and it is 2.06

x = m + z * sd

m is mean and sd standard deviation, replacing:

x = 497 + 2.06 * 109

x = 721.54

721.54 would be the minimum score.