Question

Time spent on a statistics assignment appear fairly bell shaped with a mean of 102 minutes and standard deviation of 17 minutes.

Use the empirical rule to answer the following questions:

a) Approximately 95% of the students spent between Incorrectand Incorrectminutes on the assignment.

b) Approximately 68% of the students spent between Incorrectand Incorrectminutes on the assignment.

Answer 1

The empirical rule states that for bell-shaped and symmetric data, approximately 68% falls within one standard deviation of the mean, 95% falls within two standard deviations, and more than 99% falls within three standard deviation.

Step-by-step explanation:

The empirical rule, also known as the 68-95-99.7 rule, states that for data that is bell-shaped and symmetric, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and more than 99% falls within three standard deviations of the mean.

Using this information, we can answer the given questions:

a) Approximately 95% of the students spent between 68 minutes and 136 minutes on the assignment. This is because 68 minutes is one standard deviation below the mean (102 minutes - 17 minutes) and 136 minutes is one standard deviation above the mean (102 minutes + 17 minutes).

b) Approximately 68% of the students spent between 85 minutes and 119 minutes on the assignment. This is because 85 minutes is one standard deviation below the mean (102 minutes - 17 minutes) and 119 minutes is one standard deviation above the mean (102 minutes + 17 minutes).