The average height of cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches.  Find the probability that a randomly selected cow of this breed will have a height between 56 and 60 inches.

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 between 44 and 58 inches.

An egg wholesaler wants to compare four methods of shipping eggs to determine which method results in the fewest broken eggs.  Five lots of eggs are shipped using each of the four methods.  The number of broken eggs in each lot is recorded and shown in the table below.  The wholesaler wants to determine if the average number of broken eggs is the same for each shipping method.  Therefore, he tests the null hypotheses using a 0.01 significance level. Shipping Method Sample lot no. A B C D 1 4 9 1 9 2 3 7 6 7 3 1 6 4 7 4 2 8 3 6 5 5 8 4 8 Total 15 38 18 37 Mean 3.0 7.6 3.6 7.4 What are the mean squares (MS) for treatment and error in the Analysis of Variance table given that the total SS = 122.8, treatment SS = 89.2 and error SS = 33.6?

A severe drought has affected several western states in recent years.  A Christmas tree farmer is worried about the drought’s effect on the size of his trees.  To determine whether the growth of his trees has been reduced by the drought, the farmer decides to take a sample of the heights of 6 trees and obtains the following results (recorded in inches): Tree Height 1 60 2 57 3 62 4 69 5 46 6 54 Find the variance of the heights of this sample of 6 trees.

The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones’ farm are as follows: Lamb Weight 1 30 2 32 3 28 4 42 5 40 6 44 Calculate the mean weaning weight of this sample of 6 lambs.

Suppose that 10% of the Golden Retrievers in the U.S. have a particular genetic defect.  We randomly select 6 Golden Retrievers from the population consisting of all Golden Retrievers in the U.S.  What is the probability that at least one (i.e., one or more) of the 6 dogs in the sample will have the genetic defect?  To find the answer to this question, you may use either the binomial equation or you may use the attached binomial probability table.

A study published in The Journal of American Academy of Business examined whether the perception of service quality at five-star hotels in Jamaica differs by gender.  In order to compare the means of two populations (i.e., male vs. female guests), independent random samples were selected from each population, with the results shown in the table below.  Use these data to construct a 96% confidence interval for the difference in the two population means.   Males Females Sample size 130 115 Sample mean score 39.10 38.70 Sample standard deviation 6.70 6.95

The manager of a swine operation wants to compare the litter sizes of three pigs of pigs – Duroc, Yorkshire, and Large White.  The manager obtains a random sample of litter sizes of sows of the three breeds as shown in the table below.  Use Analysis of Variance to test at the 0.05 significance level if there is a difference in the average litter sizes of the three breeds of pigs. Litter size Large White Duroc Yorkshire 10 6 11 6 7 8 8 9 13 12 4 10 6 6 10 10 12 5 6 8 6 Total 42 67 64 Average 8.4 6.7 10.7 What should the manager of the swine operation conclude regarding the average litter sizes of these three breeds of pigs?

Suppose that 20% of the Labrador Retrievers in the U.S. have a particular genetic defect.  We randomly select 7 Labs from the population consisting of all Labs in the U.S.  What is the probability that exactly 3 of the 7 dogs in this sample have the genetic defect?

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 Calculate the mean age of these 9 senior citizens.