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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?

Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours.  Further assume that the standard deviation of the times required to complete the race was 0.50 hours.  One runner completed the race in 5.0 hours.  Calculate the z-score for the runner with the time of 5.0 hours.  Based on this z-score, is this time of 5.0 hours an outlier?  Why or why not?

Suppose x has a binomial probability distribution with n = 150 and p = 0.60.  We want to determine if it is appropriate to use the normal approximation to the binomial.  Which one of the following statements is true?

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issue on the ballot.  A random sample of 500 people of voting age is selected.  Results of the poll show that 300 of the 500 people polled plan to vote in favor of the issue.  What is the point estimate of the true population proportion of people who plan to vote in favor of the issue?

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   What is the probability that a randomly selected cow either has calving difficulty or is less than 3-years-old?

The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches.  Find the probability that a randomly selected plant will have a height between 9 and 18 inches.

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

Suppose x has a binomial probability distribution with n = 200 and p = 0.70.  Use the normal approximation to the binomial to find P (X > 150).

Owners of a breed of beef cattle noted for heavy birth weights and calving difficulty would like to prove that the mean birth weight of their breed is less than 85 lb.  In other words, they want to test:      Ho:  µ = 85 lb      Ha:  µ < 85 lb They obtain a random sample of 169 birth weights of calves from this breed and find a sample mean of 83 lb and a sample standard deviation of 10 lb.  Using a significance level of 0.05, which one of the following statements is the correct conclusion?

A plant scientist wants to determine the average yield (in bushels per acre) of brand X corn in Ohio.  Five thousand Ohio corn fields are planted using brand X.  The plant scientist is able to obtain data for the yields of 500 of these 5,000 fields.  The average yield of these 500 fields planted to brand X is 175 bushels per acre.  What is the population of interest to the plant scientist?