Question

the heights of students in a class are normally distributed with mean 66 inches and standard deviation 5 inches. Use the Empirical Rule to determine the interval that contains the middle 95% of the eights Q13 a) [61, 71) b)[53, 79 x) [51, 71) Anrme d) O[51, 81 e) [56, 76 f) None of the above

Answer 1

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 66 inches and the standard deviation is 5 inches.

the interval that contains the middle 95% would fall within two standard deviations.

2 standard deviations = 2 × 5 = 10 inches

66 - 10 = 56

66 + 10 =76

Therefore, interval that contains the middle 95% is between 56 and 76 inches

Answer 2

e) [56, 76]

Explanation:

The Empirical rule states that, for a normally distributed random variable:

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

95% of the measures are within 2 standard deviations of the mean. Those are called the middle 95%.

99.7% of the measures are within 3 standard deviation of the mean. Those are called the middle 99.7%.

In this problem, we have that:

Mean 66, standard deviation 5

So the middle 95% is:

From 66 - 2*5 = 56 to 66 + 2*5 = 76

So the correct answer is:

e) [56, 76]