The heights of students in a class are normally distributed with mean 57 inches and standard deviation 7 inches. Use the Empirical Rule to determine the interval that contains the middle 68% of the heights

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 57 inches and the standard deviation is 7 inches.

the interval that contains the middle 68% of the heights would fall within one standard deviation.

1 standard deviation = 7

57 - 7 = 50

57 + 7 = 64

Therefore, the interval that contains the middle 68% of the heights would fall within 50 and 64 inches

The interval that contains the middle 68% of the heights is from 50 inches to 64 inches

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed 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:

Mean = 57

Standard deviation = 7

Use the Empirical Rule to determine the interval that contains the middle 68% of the heights

Within 1 standard deviation of the mean

57 - 7 = 50 inches

57 + 7 = 64 inches

The interval that contains the middle 68% of the heights is from 50 inches to 64 inches