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FOR INSTRUCTORS USE
| 1. a....../7 b....../7 c....../7 d....../8 | ........../29 |
| 2. a....../6 b....../6 c....../6 | ........../18 |
| 3. | ........../10 |
| 4. a....../8 b....../8 c....../10 | ........../26 |
| 5. a....../8 b....../9 | ........../17 |
| TOTAL | ........../100 |
| 1. The Hub Real Estate Investment stock is currently
selling for $16 per share. An investor plans to buy shares and hold the
stock for 1 year. Let x be the random variable indicating the price of
the stock after 1 year. The probability distribution of x shown below.
a. What is the expected price of the stock after 1 year? b. What is the expected gain per share of the stock over 1-year period? c. Find the variance and standard deviation for this probability distribution.
d. Find the probability that gain per share will be at least $3. |
| 2. The book 100% American by Daniel Evan Weiss reports over 1000 statistical facts about the United States and its people. One fact reported is that 60% of the people live in the state where they have born. |
| a. What is the probability that in a random sample of 10 people at least 8 will be living in the state where they were born? |
| b. What is the probability that in a random sample of 5 people exactly 1 person will not be living where she or he was born? |
| c. Suppose that a random sample of 100 people is
selected. Find the probability that at least half of them are living
where they were born? Use the normal approximation to find the
probability. |
| 3. A regional director responsible for business
development in Minnesota is concerned about the number of businesses that
end as failures. If the average number of failures per month is 10, what
is the probability that exactly 4 businesses will fail during a given
month? Assume that the number of businesses failing per month follows a
Poisson distribution. |
| 4. The mean cost for employee alcohol
rehabilitation programs involving hospitalization is $10,000 ((USA
Today, September 12, 1991). Assume that rehabilitation program cost
has a normal distribution with a standard deviation of $2,200. |
| a. What is the probability that a rehabilitation program will cost at least $12,000? |
| b. What is the cost range for the 10% most expensive rehabilitation programs? |
| c. If a random sample of 36 employees who used
this program has been selected, what is the probability that their
average cost will be at least $12,000? |
| 5. After a bacteria are subjected to a drug, the
length of time until the bacteria die follows an exponential distribution
with a mean of 1/2 hour. |
| a. What is the probability that bacteria will die less than 1 hour after the drug is administered? |
| b. This drug is administered to kill the bacteria in 10 different cases independently. Let |
| X= The number of cases in which the bacteria die less than 1 hour. |
| What is the probability distribution of X? |
| Find the P(X=10). |