Question

Assume a normal distribution with the average height of a sixth-grade boy is 58 inches, with a standard deviation of 2 inches.

What is the probability that a sixth-grade boy is more than 61.5 inches tall?
A. 16%.
B. 8%.
C. 4%.
D. 2%
E. 1%

Answer 1

The probability that a sixth-grade boy is more than 61.5 inches tall in a normal distribution with a mean height of 58 inches and standard deviation of 2 inches is about 4%, which corresponds to choice C.

Step-by-step explanation:

The question involves calculating the probability that a sixth-grade boy is taller than 61.5 inches given a normal distribution with an average (mean) height of 58 inches and a standard deviation of 2 inches. First, we calculate the z-score, which is the number of standard deviations a data point is from the mean. The z-score for 61.5 inches is calculated as follows:

Z = (X - μ) / σ

Z = (61.5 - 58) / 2

Z = 3.5 / 2

Z = 1.75

Then, we use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 1.75, which is approximately 0.9599. The probability of a boy being taller than 61.5 inches is 1 - 0.9599 = 0.0401 or 4%. Therefore, the correct answer is C. 4%.