The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the variance of the grades of these 8 students.

Toyota would like to know how many miles per gallon the average driver gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. Estimate the population mean for the miles per gallon of the Prius using a 90% confidence interval.

The Kimberly Clark Corporation wants to determine how many tissues a box of Kleenex should contain.  Researchers determine that 60 is the average number of tissues used by a typical person during a cold.  Suppose a random sample of 100 Kleenex users yielded a sample mean of 56 tissues and a sample standard deviation of 10 tissues used during a typical cold.  Kimberly Clark wants to test:    Ho:  μ = 60 tissues    Ha:  μ < 60 tissues using a significance level (α) = 0.05. What is the correct critical value that should be used to test the null hypothesis?

Find the probability of an observation lying more than z = 1.77 standard deviations above the mean.

The birth weights (in pounds) of 17 calves are used to construct the following stem-and-leaf display: Stem                                 Leaf                                 3             4 4 5 6            5 7            4     5     7     9 8            2     4     5     6     8     9 9            2     3     5     6     8 What is the upper quartile for this data set?

Assume that 15% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 40.

The average height of a herd of cows is 50 inches and the standard deviation of the heights is 5 inches.  Find the probability that a randomly selected cow will have a height of more than 62 inches.

A random sample of the weights of dogs at a local kennel yielded the following summary information: median = 80 lb lower quartile = 70 lb upper quartile = 90 lb lighest dog = 25 lb heaviest dog = 160 lb Use this information to construct a box plot and then use the box plot to determine which one of the following statements is true.

The mean length of time required to complete the Columbus Marathon was 4.5 hours.  The standard deviation of the times was 0.50 hours.  Assume that the racing times were approximately normally distributed.  What proportion of the runners would be expected to require between 5.0 and 5.5 hours to complete the race?

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Find the variance of the ages of these 9 senior citizens.