Question

Suppose SAT Writing scores are normally distributed with a mean of 496 and a standard deviation of 109. A university plans to award scholarships to students whose scores are in the top 7%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

Answer 1

Answer:

657

Step-by-step explanation:

We are told in the question that:

A university plans to award scholarships to students whose scores are in the top 7%.

The top 7% means

100 - 7% = 93%

These means the student must be in the 93rd percentile

We solve using the z score formula.

z = (x-μ)/σ, where

x is the raw score?

μ is the population mean = 496

σ is the population standard deviation = 109

Z score for 93rd percentile = 1.476

1.476 = x - 496/109

Cross Multiply

1.476 × 109 = x - 496

160.884 = x - 496

x = 160.884 + 496

x = 656.884

Approximately to the nearest whole number = 657

Therefore, the minimum score required for the scholarship 657