Question

Given an approximately normal distribution with a mean of 175 and a standard deviation of

37. Draw a normal curve and label 1, 2, and 3 standard deviations on both sides on the
mean. What percent of values are within the interval (138, 212)?
A. 34.196
B. 68.296
C 47.796
D. 5096

Answer 1

The question pertains to the normal distribution, where about 68% of the data lies within one standard deviation from the mean. Given the mean of 175 and a standard deviation of 37, the interval (138, 212) encompasses approximately 68% of the values, corresponding to option B, which is slightly altered but represents the correct percentage.

Step-by-step explanation:

Normal distribution and the properties of its curve are the main subjects of the question posed by the student. Given a normal distribution with a mean (μ) of 175 and a standard deviation (σ) of 37, we look to identify the percentage of values within the interval (138, 212). According to the Empirical Rule, approximately 68% of the data within a normal distribution is found within one standard deviation from the mean on either side.

In the scenario described, one standard deviation from the mean extends from (μ - σ) 175 - 37 = 138 to (μ + σ) 175 + 37 = 212. Therefore, the interval (138, 212) corresponds to the range within one standard deviation from the mean. According to the Empirical Rule, this encompasses about 68% of the data, which aligns with option B, 68.26%.

Note: The percent provided in choice B is slightly altered but is meant to represent 68%, which is consistent with the Empirical Rule and the correct answer to the problem.