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.
Thirtyfive 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
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 5minute 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
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