1)A die is continuously rolled until the total sum of all rolls exceeds 250. What is the probability that at least 75rolls are necessary?

2)

Let us suppose that a certain probability instructor manages, with probability 1, to write exams that have mean 60 and standard deviation 15. The instructor is teaching two classes, one of size 81 and the other of size 16, and is about to give an exam to both classes.

(a) Approximate the probability that the average test score in the class of size 81 exceeds 65. Probability

(b) Repeat part (a) for the class of size 16. Probability

(c) Approximate the probability that the average test score in the larger class exceeds that of the other by more than 1.6 points. Probability

(d) Approximate the probability that the average test score in the smaller class exceeds that in the other by more than 1.6 points. Probability

3)

A variable of two populations has a mean of 46 and a standard deviation of 13 for one of the populations and a mean of 51 and a standard deviation of 10 for the other population.

a) For independent samples of sizes 48 and 57, respectively, find the mean and standard deviation of x1x2. mean: standard deviation:

b) Can you conclude that the variable x1x2 is approximately normally distributed? (Answer yes or no) answer: