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A farmer wants to determine if any of the pigs that he just finished weighing are outliers.  The average weight of the pigs was 240 lb and the standard deviation of the weights was 35 lb.  According to his records, one of the pigs weighed 520 lb.  Calculate the z-score for this pig.  Based on this z-score, is the weight of 520 lb an outlier?

On a particular ranch weaning weights of calves are normally distributed with a mean of 430 lb and a standard deviation of 20 lb.  Find the probability that a randomly selected calf will weigh less than 415 lb.

Assume that you own a herd of Bison.  By plotting the birth weights of the calves born in your herd in the spring calving season, you determine that the distribution of birth weights was symmetric and mound-shaped with a mean of 80 lb and a standard deviation of 10 lb.  You would expect that approximately 95% of the calves born in your herd during the spring calving season would have birth weights between __________ and __________ lb.

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.

Psychologists at the University of Minnesota compared the scores of independent random samples of male and female 8th grade students who took a basic skills math achievement test to determine if males outperform females in math.  A summary of the test score data is shown below:                                            Males          Females     Sample size                         1,764            1,739 Sample means                      48.9              48.4 Sample standard deviations  12.96          11.85                                                                                  Use a 90% confidence interval to estimate the true difference in mean test scores between males and females.

Scientists are interested in determining if the mean alkalinity level of water specimens from the Han River in Seoul, Korea is greater than 50 milligrams per liter (mpl).  They select a random sample of 100 water specimens from the river and find a sample mean of 70 mpl and a sample standard deviation of 15 mpl.  They decide to test the hypothesis that the population mean for alkalinity level of water in the Han River exceeds 50 mpl using a significance level of 0.01.  Find the value of the test statistic used to test this hypothesis.

It is desired to estimate the proportion of cows conceiving at first service (breeding) in an artificial insemination (AI) program used on a particular farm.  A random sample of 50 cow records is chosen; 30 of these 50 cows conceived at first service.  Construct a 95% confidence interval for the true population proportion of cows conceiving at first service on this farm.  You can assume that large-sample procedures are appropriate.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school district.  A random sample of 400 people of voting age is selected.  Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy.  Construct a 99% confidence interval for the true population proportion of people who plan to vote in favor of the school levy.

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

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd.  He constructs the following table:                             Age of Cow (in years)                                           0-2     3-5     6-10     over 10   Total No difficulty     40      35       20          5            100 Difficult birth   35      45       15          5            100 Total                  75      80       35        10           200   Given that the randomly selected cow had no difficulty in giving birth to her calf, what is the probability that she was more than than 2 yr old?