(7) If the probability of a student graduating is 0.95, find the probability that more than 472 students students graduating among 500 students.   (8) If the probability of a student receiving financial aid is 0.72, find the mean and variance of the number of students receiving financial aid among 40000 students.   (9) There are 300 questions on a multiple choice exam. For each question there are 5 choices to choose from, and there is only one correct choice for each question. Find the mean (expected value) and variance for the number of questions you answer correctly by making random guess.

The owner of a chain of mini-markets has two stores, Store 1 and Store 2, in one city. She recently added a breakfast station in Store 1 and wants to determine if the mean daily sales of Store 1 is greater than the mean daily sales of Store 2. After choosing 12 days at random, she records the sales (in dollars) at Store 1 for these days. Then, she records the sales at Store 2 for these same days. The data and the differences (Store 1 minus Store 2) are shown in the table below. Day 1 2 3 4 5 6 7 8. 9. 10 11 12 Store 1 951 547 437 682 547 729 488 776 461 815 859 518 Store 2 989 599 500 680 451 528 452 741 446 758 960. 421 Difference (Store 1 − Store 2) −38 −52 63 2 96 201. 36 35 15 57 −101 97 Send data to calculator Send data to Excel (a)Are the two samples of daily sales amounts independent or paired…

A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 12.4. In his class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 7 students or more will score an "A" on the final exam?

A racing car consumes a mean of 103 gallons of gas per race with a variance of 36. If 38 racing cars are randomly selected, what is the probability that the sample mean would be greater than 101.5 gallons? Round your answer to four decimal places.