Problem 1. The goal at U.S airports handling international flights is to clear these flights in 45 minutes. Lets interpret this to mean that 95% of the flights are cleared in 45 minutes, so 5% of the flights take longer to clear. Lets also assume that the distribution is approximately normal.
a. if the standard deviation of the time to clear an international flight is 5 minutes, what is the mean time to clear a flight?
b. suppose the standard deviation is 10 minutes, not the 5munites suggested in part (a). what is the new mean?
c. a customer has 30 minutes from the time her flight lands to catch a limousine. Assuming a standard deviation of 10 minutes, what is the likelihood that she would be cleared in time?
Problem 2. Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79,64,84,82,92 and 77. Instead of averaging the six scores, the instructor indicated that he would randomly select 2 grades and compute the final percent correct based on the two percents.
a. how many different samples of two test grades are possible?
b. list all possible samples of size two and compute the mean of each.
c. compute the mean of the sample means and compare it to the population mean.
d. if you were a student, would you like this arrangement? Would the rest be different from dropping the lowest score? Write a brief report.
Problem 3. Over the past decade the mean number of members of the information system securities association who have experienced a denial-of-service attack each year is 510 with a standard deviation of 14.28 attacks. Suppose nothing in this environment changes.
a. what is the likelihood this group will suffer an average of more than 600 attacks in the next 10 yrs?
b. compute the probability the mean number of attacks over the next 10 yrs is between 500 and 600.
c. what is the possibility they would experience an average of less than 500 attacks over the next 10 yrs?