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Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 70 inches and a standard deviation of 10 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a point estimate.

Medical research has shown that a certain type of chemotherapy is successful 70% of the time when used to treat skin cancer.  Suppose 5 skin cancer patients are treated with this type of chemotherapy.  Let X equal the number of patients out of 5 who are cured.  The probability distribution for the number of patients out of 5 who are cured is given in the following table:                                                                                         X             0           1           2           3           4           5     P (X)    0.002   0.029   0.132    0.309    0.360    0.168       Find μ = E [X].

It seems reasonable to assume that ovulation rate and litter size in pigs would be positively correlated.  In other words, if a sow releases more eggs (i.e., ova) in a given estrus period, she will probably end up producing more pigs in her litter.  Number of eggs ovulated and litter size for a random sample of 6 sows are as follows: Number of Eggs, X       Number of Pigs Born, Y                14                                  7                15                                  7                16                                  9                17                                 10                17                                 10                17                                  11 Calculate the covariance between variables X and Y.

If the variation between sample means is large relative to the variation within the samples, it indicates that there is a real difference between the population means.

Quantitative data are

A random sample of sale prices of homes in Columbus, Ohio yielded the following summary information:      Median = $125,000     Lower quartile = $82,000     Upper quartile = $168,000      Lowest price = $46,000     Highest price = $276,000 Construct a box plot for these data.  Based on this box plot, is the highest selling price of $276,000 a suspect or highly suspect outlier?

An animal scientist wants to determine the degree of association between carcass quality grade (variable X) and selling price per pound of carcass (variable Y).  The data for a random sample of 10 Angus steer carcasses are shown in the following table. Quality grade, X Carcass price per pound, Y 5 $1.09 7 1.19 4 0.99 5 1.04 8 1.21 6 1.18 4 0.94 7 1.15 8 1.23 6 1.12 Find the covariance between carcass quality grade and carcass price per pound.

Suppose that a random sample of 625 measurements is selected from a population with a mean µ = 500 lb and a variance σ2 = 100 lb2.  What is the mean and standard deviation of the sampling distribution of the sample mean?

Suppose that a scientist has 60 mice that he could use in an experiment involving a new drug to treat a certain disease.  The scientist decides to use 6 of the 60 available mice for a small preliminary experiment before conducting a larger study.  The scientist arbitrarily begins at row 20 column 1 of the random number table and goes from left to right across the row.  Which one of the following is the correct random sample of 6 mice? For your convenience, here are rows 20 and 21 of the random number table:       Column       Row 1 2 3 4 5 6 20 07056 97628 33787 09998 42698 06691 21 48663 91245 85828 14346 09172 30168

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 is the probability that a randomly selected runner completed the race in less than 3.6 hours?