Question

"A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class

Answer 1

Answer:

43.05, meaning a score of 43

Step-by-step explanation:

Answer 2

Answer: the cutoff score to get into the class is 43

Step-by-step explanation:

Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = scores on the test.

µ = mean score

σ = standard deviation

From the information given,

µ = 38

σ = 6

The probability value for the 80th percentile is 80/100 = 0.8

Looking at the normal distribution table, the z score corresponding to the probability value is 0.85

Therefore,

0.85 = (x - 38)/6

Cross multiplying by 6, it becomes

0.85 × 6 = x - 38

5.1 = x - 38

x = 5.1 + 38

x = 43.1

Approximately 43