2024 – 1 Assume you have data set from a normally distributed random variable Answer the following questions a Will

1. Assume you have data set from a normally distributed random variable. Answer the following questions: a. Will the random variable be discrete, continuous, or neither? How do you know? b. Will the data be qualitative or quantitative? How do you know? 2. A university has been tracking the percentage of alumni giving to its annual fund each year for the past 10 years. The data is given below: 14% 13% 15% 21% 19% 24% 25% 28% 25% 31% Answer the following questions: a. What are its mean and media? 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 median computed in part a. 3. Under which of the following conditions would be appropriate to use a Binomial random variable? 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 suggests 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 or 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. 4. The mean time for a race car 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? 5. a random sample for 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 p at the 95% confidence level? 6. 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 that 20 students in his class will have 3 cavities.