Question

1. the heights of students are distributed normally with a mean of 58\ and standard deviation of 3\. approximately 68% of students are between what heights?

a) 55\ and 61\ b)52\ and 64\ c)49\ and 67\ d)46\ and 70\
options: d, c, a, b

Explanation:

Step1: Recall the empirical rule

For a normal distribution, approximately 68% of the data lies within 1 standard deviation of the mean. The formula is \( \mu - \sigma \) to \( \mu + \sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.

Step2: Identify \( \mu \) and \( \sigma \)

Here, \( \mu = 58'' \) and \( \sigma = 3'' \).

Step3: Calculate the bounds

Lower bound: \( 58 - 3 = 55'' \)
Upper bound: \( 58 + 3 = 61'' \)

Answer:

A. \( 55'' \) and \( 61'' \)