The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following question. A quantitative data set of size 100 has mean 50 and standard deviation 4. Approximately how many observations lie between 38 and 62 ?

Approximately 100 lie between 38 and 62.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed (bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

100 observations.

Mean = 50

Standard deviation = 4

Approximately how many observations lie between 38 and 62 ?

38 = 50 - 4*3

38 is three standard deviations below the mean

62 = 50 + 4*3

62 is three standard deviations above the mean

By the Empirical Rule, 99.7% of the measures are within 3 standard deviations of the mean.

There are 100 observations.

0.997*100 = 99.7

Approximately 100 lie between 38 and 62.