The Central Limit Theorem is important in statistics, because:

Assume X is a binomial random variable.  If n = 15 and p = 0.60, find P (r ≤ 5 successes).

The t and z distributions are very similar.  Both are symmetric, mound-shaped, and have a mean of zero.

The computer science department wants to estimate the average length of time it takes students to complete a computer project correct to within 5 hours with probability 0.96.  They do not have an estimate of the standard deviation of the times, but they remember that last year the shortest time needed to complete the project was 6 hours and the longest time was 36 hours.  Given this information, an appropriate estimate of the standard deviation of the length of time required to complete the computer project would be:

One difference between a randomized block experiment and a factorial experiment is that a randomized block experiment only has one observation per cell, whereas a factorial experiment almost always has more than one observation per cell.

The American Journal of Public Health published a study of the relationship between passive smoking and nasal allergies in Japanese female students.  The study revealed that 80% (i.e., p = 0.80) of the students from heavy-smoking families showed signs of nasal allergies on physical examinations.  Consider a sample of 10 Japanese female students exposed daily to heavy smoking in their families.  What is the probability that exactly 8 of the 10 students will have nasal allergies?

We are interested in comparing the mean supermarket prices of two leading colas in the Columbus area.  Assume that we have independent random samples of prices of six-packs at 8 supermarkets.  The data are shown in the following table: Supermarket      Brand 1       Brand 2  1                             $2.25          $2.30 2                               2.47            2.45 3                               2.38            2.44 4                               2.27            2.29 5                               2.15            2.25 6                               2.25            2.25 7                               2.36            2.42 8                               2.37            2.40 _______________________________________ Mean                       $2.3125       $2.3500 Standard deviation  $0.1007       $0.0859 _______________________________________ Find a 98% confidence interval for the difference in mean price of Brand 1 and Brand 2, assuming that these are independent random samples.

Assume that a 90% confidence interval for the mean weight of the population consisting of male students attending OSU is (150 lb,  200 lb).  What is the meaning of this 90% confidence interval?

If the lower quartile is farther from the median than the upper quartile, the distribution of data is

In a controlled laboratory environment, independent random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable.  The study provided the following results:                                               Adults         Children Sample size                            10                 10 Sample mean (in degrees)   77.5              74.5 Sample variance                       4.5                2.5 Which one of the following is the correct 99% confidence interval for the true difference in population mean temperatures that adults and children find most comfortable?