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A farm supply store manager wants to predict monthly sales, Y, for her company using advertising expenditures, X.  She has collected 10 months of data on past performance as shown in the following table. Advertising expenditures, in thousands of dollars, X Monthly sales, Y XY X2 Y2 1.2 101 121.2 1.44 10,201 0.8 92 73.6 0.64 8,464 1.0 110 110.0 1.00 12,100 1.3 120 156.0 1.69 14,400 0.7 90 63.0 0.49 8,100 0.8 82 65.6 0.64 6,724 1.0 93 93.0 1.00 8,649 0.6 75 45.0 0.36 5,625 0.9 91 81.9 0.81 8,281 1.1 105 115.5 1.21 11,025 TOTAL 9.4 959 924.8 9.28 93,569 The store manager performs a regression analysis and derives the following equation. Y =

A physical fitness association is including the mile run in its secondary-school fitness test for boys.  The time for this event for boys in secondary school is known to have a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds.  The fitness association wants to recognize the fastest 10% of the boys with a certificate of achievement.  What time would the boys need to beat in order to earn a certificate of achievement from the fitness association?

A population of rabbits has a mean weight of 10 lb and a standard deviation of the weights equal to 2 lb.  A rabbit breeder selects a large number of samples of 100 rabbits each, calculates the mean weight of the rabbits in each of these samples, and then graphs the sample means. The mean of these sample means is expected to be equal to _______.

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 correlation between carcass quality grade and carcass price per pound.

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?