Question

A standardized test has a mean of 110 points and a standard deviation of 10 points. John scored at the 98th percentile on the test. Find his score to the nearest whole number.

Answer 1

Answer: his score 131 points

Step-by-step explanation:

Assuming the scores in the standardized test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = standardized test scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 110 points

σ = 10 points

Looking at the normal distribution table, the z score that corresponds to the 98 percentile is 2.06

2.06 = (x - 110)/10

Cross multiplying, it becomes

2.06 × 10 = x - 110

2.06 = x - 110

x = 20.6 + 110

x = 130.6

Approximately, x = 131