ANSWER ALL QUESTION IN THE SPACE PROVIDED. SHOW YOUR WORK WHERE APPLICABLE.LNDICATE YOUR ANSER CLEARLY. EACH QUESTION IS WORTH 25 POINTS.

1.1.In a class of 15 students, the probability that a student will the final exam is 85%.

(a)What is the probability that exactly 10 students will pass?

(b)Find the probability that at least 13 students will pass the final exam.

(c) Find the probability that at most 8 students will pass the final exam.

(d) Find the Expected value ( the population mean )""

(e) the standard deviation

2. A public speaker computes the probabilities for the number of speeches she gives in a week.The distribution is as follows: Find the mean, variance and the standard deviation for the distribution.

Number of speeches

0

1

2

3

4

Probabilities

.10

.44

.23

.21

.02