## The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats.

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Question 3. The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a PROBABILITY TREE, determine the probability that the bill will pass.

Question 4. The following probabilities for grades in Statistics course have been determined

based on past records:

Grade Probability

 A .1 B .3 C .4 D .1 F .1

The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.

Question 5. Consider a binomial experiment with n = 10 and p = 0.10. Use the binomial tables below  to answer parts (a) through (d).

a)      Find f (0).

b)      Find f (2).

c)      Find P(x 2).

d)     Find E(x).

e)      Find Var(x) and

Question 6. Telephone calls arrive at the rate of 48 per hour at the reservation desk for Regional

Airways.

a.       find the probability of receiving 3 calls in a 5-minute interval.

b.      find the probability of receiving 10 calls in 15 minutes.

c.       Suppose that no calls are currently on hold. If the agent takes 5 minutes to complete processing the current call, how many callers do you expect to be waiting by that time? what is the probability that no one will be waiting?

d.      If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted?

Question 7.  Consider a Poisson probability distribution with 2 as the average number of occurrences per time period.

a)      write the appropriate Poisson probability function.

b)      what is the average number of occurrences in three time periods?

c)      write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.

d)     find the probability of two occurrences in one time period.

e)      find the probability of five occurrences in two time per