1. A university has been tracking the percentage of alumni giving to its annual fund each for the past 10 years. The data is given here.
14% 13% 15% 21% 19% 24% 25% 28% 25% 31%
Answer the following questions about this data.
a. What are its mean and median?
b. What is the procedure for using mean and median to determine whether the data is skewed, and if so, in what direction?
c. Apply the procedure you described to the mean and media computed in part a.
2. Under which of the following conditions would it be appropriate to use a Binomial randomvariable? In each case, explain why your answer is correct.
a. A department will interview 10 candidates for a position, and call back for second interviews those who answer the interview questions to the satisfaction of all the interviewers. They hope to call back at least 3, but past experience suggest an average of about 1 call back per 4 interviews.
b. A factory posts on the wall the number of days since its last safety infraction of injury. In the past year, the factory has had a safety infraction or injury on 6 different days. The factory is interested in the number of days that can be expected to elapse without an injury.
c. Fifteen of a doctor's patients have the same ailment. Studies have shown that about 86.5% of patients with this ailment respond to a certain drug. The doctor prescribes the drug to all 15, but the number who will respond in this case is, of course, not known in advance.
3. The mean time for a racecar driver's crew to perform a pit stop is 13.2 seconds, with a standard deviation of 0.9 seconds. To maintain his current lead, the driver needs a pit stop in 12.5 seconds or less. Assuming this random variable is normally distributed, what is the probability of the driver getting the pit stop in a short enough time to maintain his lead?
4. A random sample from the population of registered voters in California is to be taken and then surveyed about an upcoming election. What sample size should be used to guarantee a sampling error of 3% or less when estimating pat the 95% confidence level?
5. An elementary school teacher learned that 40% of school children have at least three cavities. The teacher has 30 students in his class. How many students would he expect in his class to have at least three cavities? What is the standard deviation? Using the appropriate approximation, determine P(x > 20); that is the probability that more than 20 students in his class will have 3 cavities.