The mean weaning weight in a herd of beef cattle is 520 lb and the standard deviation of the weaning weights is 50 lb.  What is the probability of a calf weighing more than 600 lb?

The Animal Sciences Department wants to estimate the average length of time it takes students to complete a class project correct to within 5 hours with a 98% level of confidence.  Determine the sample size needed to estimate the average length of time required to complete the project to within 5 hours with a 98% level of confidence if the standard deviation of the times is 4 hours.

The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the range for the grades of these 8 students.

It seems reasonable to assume that the number of times a team punts the ball in a football game would be negatively correlated with the number of points that the team scores (i.e., if a team is forced to punt frequently they are probably not moving the ball very well and probably are not scoring many points).  Number of punts (variable X) and number of points scored (variable Y) for a particular team in a random sample of five games are as follows: Number of Punts, X          Number of Points, Y              2                                         35              5                                         14              3                                         21              2                                         21              2                                         28   We want to test our assumption of a negative correlation between number of punts and number of points scored in a football game.  State the appropriate null and alternative hypothesis.  Using a significance level of 0.05, do you reject or not reject the null hypothesis?  Why?

The probability of a male offspring is 1/2 and the probability of a female offspring is 1/2.  What is the probability that a mare will give birth to a female offspring in four consecutive years, assuming that the sexes of the offspring in different years are independent events?

In order to compare the means of two populations, independent random samples are selected from each population, with the results shown in the table below.  Use these data to construct a 98% confidence interval for the difference in the two population means.   Sample 1 Sample 2 Sample size 400 400 Sample mean 5,275 5,240 Sample standard dev. 150 200

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       Find the F value for the line x breed interaction.

In order to compare the means of two populations, independent random samples are selected from each population, with the following results:                                             Sample 1     Sample 2 Sample size                            500                400 Sample mean                       5,280             5,240 Sample standard deviation     150                200 Construct a 95% confidence interval for the difference in the two population means.

The body weight in pounds (variable X) and fleece weight in pounds (variable Y) of a random sample of four ewes are as follows: Body weight, lb (X)            Fleece weight, lb (Y)           140                                            9           145                                          10           155                                          10           160                                          12                                                                                      Derive the equation for the regression line.  What would be the predicted fleece weight of a ewe that weighs 152 lb?

The Central Limit Theorem is important in statistics, because: