Question

The measurement of the height of 600 students of a college is normally distributed with a mean of 175 centimeters and a standard deviation of 5 centimeters. What percent of students are less than 170 centimeters in height?

A. 16.0%
B. 2.0%
C. 0.5%
D. 15.5%

Answer 1

The percentage of students less than 170 centimeters tall is approximately 16%, which corresponds to a z-score of -1 in the standard normal distribution. The correct answer is A. 16.0%.

Step-by-step explanation:

The student asked what percent of students are less than 170 centimeters tall if the height of 600 students at a college is normally distributed with a mean of 175 centimeters and a standard deviation of 5 centimeters.

To answer this question, we need to calculate the z-score for 170 centimeters using the formula z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Substituting the given values, we have:

z = (170 - 175) / 5 = -5 / 5 = -1.

A z-score of -1 corresponds roughly to the 16th percentile in the standard normal distribution, which indicates that approximately 16% of the students are less than 170 centimeters tall. Therefore, the correct answer is A. 16.0%.