Question

suppose ACT Mathematics scores are normally distributed with a mean of 21.3 and a standard deviation of 5.3. A university plans to send letters of recognition to students whose scores are in the top 11%. What is the minimum score required for a letter of recognition

Answer 1

Answer: the minimum score required for a letter of recognition is 27.8

Explanation:

Suppose ACT Mathematics scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = ACT Mathematics scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 21.3

σ = 5.3

The probability of students whose scores are in the top 11 % would be be (1 - 11/100) = (1 - 0.11) = 0.89

Looking at the normal distribution table, the z score corresponding to the probability value is .23

Therefore,

1.23 = (x - 21.3)/5.3

Cross multiplying by 8.6, it becomes

1.23 × 5.3 = x - 21.3

6.519 = x - 21.3

x = 6.519 + 21.3

x = 27.8 to the nearest whole number