Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

1 The monthly sales of mufflers follow the normal distribution with a mean of 1250 and a standard deviation of 255. The manufacturer would like to establish inventory levels such that there is only a 2% chance of running out of stock. Refer to the table in Appendix B.1.  

Where should the manufacturer set the inventory levels?

part B

1 The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 11,300. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 680 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. Refer to the table in Appendix B.1.  

How many pages should the manufacturer advertise for each cartridge if it wants to be correct 95 percent of the time? (Round z-value to 2 decimal places and the final answer to the nearest whole number.)

Pages           

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding the null hypothesis?

4. What is the p-value? (Round your answer to 3 decimal places.)

6. A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of the trip-length to be normally distributed. (a) If the office opens at 9:00am and he leaves his house at 8:40 am daily, what percentage of the time is he late for work? You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number. (b) Find the length of time above which we find the longest 20% of the trips. You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number. (c) During a period of 20 work days, on how many days should you expect the lawyer to be late for work? (d) What is the probability that he is late on at most 10 of those 20 days?

1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:

The correlation between the fund returns is 0.15.

What is the Sharpe ratio of the best feasible CAL?

Sharpe ratio=

2. The standard deviation of the market-index portfolio is 10%. Stock A has a beta of 2.50 and a residual standard deviation of 20%.


a. Calculate the total variance for an increase of 0.10 in its beta. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

b. Calculate the total variance for an increase of 1.24% in its residual standard deviation. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Your company faces a 34% tax rate and has $258 million in assets, currently financed entirely with equity. Equity is worth $8.80 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below: State Pessimistic Optimistic Probability of State .25 .75 Expect EBIT in State $10.8 million $50.8 million The firm is considering switching to a 20-percent debt capital structure, and has determined that they would have to pay a 9 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? (Round your intermediate calculations and final answer to 2 decimal places, except calculation of number of shares which should be rounded to nearest whole number.)

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

Your company doesn't face any taxes and has $258 million in assets, currently financed entirely with equity. Equity is worth $8.8 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below:

State Pessimistic Optimistic

Probability of State .25 .75

Expect EBIT in State $18 million $58 million

The firm is considering switching to a 20-percent debt capital structure, and has determined that they would have to pay a 9 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? (Round your intermediate calculations and final answer to 2 decimal places except calculation of number of shares which should be rounded to nearest whole number.)

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

A binomial probability distribution has p = 0.25 and n = 81.

A) What are the mean and standard deviation?

B) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.

C) What is the probability of exactly 28 successes?

D) What is the probability of 18 to 22 successes?

E)What is the probability of 24 or fewer successes?