7. Assume that the salaries of elementary school teachers in the U.S. are:

Normally distributed

Mean: $26,000

Standard deviation: $5,000

What is the cutoff salary for teachers in the bottom 10%?

**Solution: **First we find the bottom 10% for z-scores. We need to find_{}such that

_{}

Using the inverse cumulative normal distribution we find that_{} . The cutoff salary for teachers in the bottom 10% is

_{}

8. Farmers sell fruits and vegetables at roadside stands during the summer.

Normally distributed

Mean: 405 tomatoes/day

Standard deviation: 30 tomatoes/day

If there are 363 tomatoes available to be sold at the stand at the beginning of a day, what is the probability that they will all be sold?

**Solution: **Let_{}be the number of tomatoes that are sold, then

_{}

9. The amount of time it takes a student to walk from her home to class has a:

Skewed right distribution

Mean: 16 mins.

Standard deviation: of 1.6 mins. If data were collected from 30 randomly selected walks, describe the sampling distribution of the sample mean time.

**Solution: **Assuming normality, the sample mean time as a mean of 16, and a standard deviation of_{}. Therefore,

_{}