Question

The mean and the standard deviation of a sample of 65 customer satisfaction ratings are 45.96 and 4.21, respectively. Use the empirical rule to calculate estimates of a tolerance interval containing 95.44 percent of all possible satisfaction ratings.

Answer 1

The empirical rule states that approximately 95 percent of the data in a bell-shaped distribution falls within two standard deviations of the mean. To calculate a tolerance interval containing 95.44 percent of all possible satisfaction ratings, we can use the formula: Tolerance Interval = (Mean - (Z * Standard Deviation), Mean + (Z * Standard Deviation)). In this case, the tolerance interval is (34.045, 57.875).

Step-by-step explanation:

The empirical rule states that in a bell-shaped distribution, approximately 95 percent of the data will fall within two standard deviations of the mean.

To calculate the tolerance interval containing 95.44 percent of all possible satisfaction ratings, we can use the formula:

Tolerance Interval = (Mean - (Z * Standard Deviation), Mean + (Z * Standard Deviation))

Where Z is the number of standard deviations from the mean that corresponds to the desired percentage. In this case, Z is 2.5 because we want to capture 95.44 percent of the data. Therefore, the tolerance interval is (45.96 - (2.5 * 4.21), 45.96 + (2.5 * 4.21)) = (34.045, 57.875).