Question

Final exam scores in a statistics class were normally distributed with a μ = 65 and a standard deviation σ = 5. What is the probability that a randomly selected student will score 70 or higher?

A) 16%
B) 68%
C) 84%
D) 32%

Answer 1

The probability that a randomly selected student will score 70 or higher on the final exam is approximately 16%, which corresponds to Option A.

Step-by-step explanation:

To find the probability that a randomly selected student will score 70 or higher on a statistics final exam with a mean (μ) of 65 and a standard deviation (σ) of 5, we will use the properties of the normal distribution.

First, we calculate the z-score for a score of 70:

Z = (X - μ) / σ

Z = (70 - 65) / 5

Z = 1

A z-score of 1 indicates that a score of 70 is one standard deviation above the mean. Since the normal distribution is symmetric, the area to the left of z = 1 is 0.8413 (or 84.13%). Therefore, the area to the right of z = 1, which represents the probability of scoring higher than 70, is 1 - 0.8413, which equals 0.1587 or approximately 16%.

This information gives us the answer: Option A) 16%