Question

Students at a liberal arts college study for an average of 10 hours per week with a standard deviation of 2 hours per week. The distribution of their study time happens to be uni-modal, symmetric and bell shaped. Approximately 68% of students study between 8 and B hours a week. What is the value of B

Answer 1

it lies between 8 hours and 12 hours in a week

Explanation:

Since in the question it is mentioned that the distribution consist of uni-modal, symmetric and bell shaped so here the empirical formual to be used for the mean and the standard deviation

Also the 68% would be fall within one standard deviation above and below the mean

Now

1 standard deviation below the mean is

`= \mu - \sigma`

= 10 - 2

= 8 hours

And, above the mean is

`= \mu + \sigma`

= 10 + 2

= 12 hours

Hence, it lies between 8 hours and 12 hours in a week