Question

The number of hours college students spend working per week has a normal distribution with a mean of 22 hours and a standard deviation of 6 hours. Determine the percentage of college students who work between 16 and 28 hours per week.

Answer 1

A raw score of 16 when converted to a z-score is z = (16 - 22)/6 where 22 is the sample mean and 6 is the standard deviation. z = -6/6 =-1 which means that a score of 16 is one standard deviation unit below the mean.

A raw score of 28 when converted to a z-score is z = (28 - 22)/6 = 6/6 = 1 standard deviation above the mean.

From the standard normal distribution table, .3413 of the area under the curve corresponds to the region between z = -1 and z = 0, the mean. Because the standard normal curve is symmetric about its mean, the area between z = 0 and z = 1 is also .3413.

The region under the curve and bounded by z = -1 and z = 1 is .3413 + .3413 = .6826.
68.26% of the college students work between 16 and 28 hours a week.