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,
