The annual per capita consumption of bottled water was

31.531.5

gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of

31.531.5

and a standard deviation of

1212

gallons.a. What is the probability that someone consumed more than

3232

gallons of bottled​ water?b. What is the probability that someone consumed between

2525

and

3535

gallons of bottled​ water?c. What is the probability that someone consumed less than

2525

gallons of bottled​ water?d.

9999​%

of people consumed less than how many gallons of bottled​ water?

a. The probability that someone consumed more than

3232

gallons of bottled water is

nothing.

​(Round to four decimal places as​ needed.)

b. The probability that someone consumed between

2525

and

3535

gallons of bottled water is

nothing.

​(Round to four decimal places as​ needed.)

c. The probability that someone consumed less than

2525

gallons of bottled water is

nothing.

​(Round to four decimal places as​ needed.)

d.

9999​%

of people consumed less than

nothing

gallons of bottled water.

​(Round to two decimal places as​ needed.)

Population of United States is 312 million people

a) What is the probability that an American chosen at random died as a passenger car occupant last year?

b) What is the probability that you died as a passenger car occupant last year? Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)

c) Estimate the probability that you will die as a passenger car occupant next year?

d) What is the probability that an American chosen at random will die as the result of a tornado next year?

e) Estimate the probability that you will die as the result of a tornado next year?

f) Why is this answer different than the probability for an American chosen at random?

g) People sometimes claim skydiving is less dangerous than driving or riding in a car. Does the data support this claim? Explain.

h) People sometimes claim motorcycle riding is less dangerous than traveling by car. Does the data support this claim? What additional information and/or calculations would be useful to evaluate this claim?

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be A. collectively exhaustive. B. the sample space. C. mutually exclusive. D. independent. (b) If event A and event B are as above and event A has probability 0.2 and event B has probability 0.2, then the probability that A or B occurs is ____

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 61 percent BLUE, 21 percent RED, and 18 percent GREEN.

(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

Compute the expected return and standard deviation for the following properties. The current price of each property is $500,000. Which has the better risk-return tradeoff?

Property A:

• Pessimistic: NOI stays flat at $50,000 per year for the next 5 years. Resale price is $500,000 in year 5. Probability = 25%.
• Most Likely: NOI starts at $50,000 the first year and grows by 1% for the next 5 years. Resale price is $525,000 in year 5. Probability = 50%.
• Optimistic: NOI starts at $50,000 the first year and grows by 3% for the next 5 years. Resale price is $575,000 in year 5. Probability = 25%.

Property B:

• Pessimistic: NOI starts at $50,000 the first year and decreases by 2% for the next 5 years. Resale price is $475,000 in year 5. Probability = 25%.
• Most Likely: NOI starts at $50,000 the first year and grows by 1% for the next 5 years. Resale price is $525,000 in year 5. Probability = 50%.
• Optimistic: NOI starts at $50,000 the first year and grows by 5% for the next 5 years. Resale price is $600,000 in year 5. Probability = 25%.

What's your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 30% of ice cream sales are vanilla. Chocolate accounts for only 13% of ice cream sales. Suppose that 174 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. (Round your answers to four decimal places.)

(a) What is the probability that 50 or more will buy vanilla?

(b) What is the probability that 12 or more will buy chocolate?

(c) A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? Hint: Chocolate flavor and vanilla flavor are not mutually exclusive events. Assume that the choice to buy one flavor is independent of the choice to buy another flavor. Then use the multiplication rule for independent events, together with the addition rule for events that are not mutually exclusive, to compute the requested probability.

d) What is the probability that between 50 and 60 customers will buy chocolate or vanilla ice cream? Hint: Use the probability of success computed in part (c).

In​ mid-2009, Rite Aid had​ CCC-rated,

11

​-year

bonds outstanding with a yield to maturity of

17.3 %

.

At the​ time, similar maturity Treasuries had a yield of

4 %

.

Suppose the market risk premium is

5 %

and you believe Rite​ Aid's bonds have a beta of

0.32

.

The expected loss rate of these bonds in the event of default is

56 %

.

a. What annual probability of default would be consistent with the yield to maturity of these bonds in​ mid-2009?

b. In​ mid-2015, Rite-Aid's bonds had a yield of

7.2 %

​,

while similar maturity Treasuries had a yield of

1.6 %

.

What probability of default would you estimate​ now?

a. What annual probability of default would be consistent with the yield to maturity of these bonds in​ mid-2009?

The required return for this investment is

nothing

​%.

​ (Round to two decimal​ places.)

The annual probability of default is

nothing

​%.

​ (Round to two decimal​ places.)

b. In​ mid-2015, Rite-Aid's bonds had a yield of

7.2 %

​,

while similar maturity Treasuries had a yield of

1.6 %

.

What probability of default would you estimate​ now?

The probability of default will be

nothing

​%.

​(Round to two decimal​ places.)

A service process has three serial stages. The defect percentage at stage one is 16%. The defect percentage at stage two is 13%. And, the defect percentage at stage three is 10%. Use 3 decimals for probabilities in the following situations. (a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (d)[3] Give some possible real‐life processes for the three situations above.

A study is conducted to survey (in thousands) of earned degrees in the United States in a recent year. The table is given below.

a) If one person is randomly selected, find the probability that this person is a female.      

  b)  If one person is randomly selected, find the probability that this person has a bachelor degree and is a male.   

  c)   If one person is randomly selected, find the probability that this person has an AA degree.  

d) If one person is randomly selected, find the probability that this person is a female, giventhat the person received an AA degree.

e) If one person is randomly selected, find the probability that this person has a master degree or is a female.

f) Are the events “female” and “AA degree” independent? Why or why not? Use the answers from a) and d) above to explain this.

g) If two people are randomly selected, find the probability that these two people are males.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you take the free samples offered in supermarkets? About 64% of all customers will take free samples. Furthermore, of those who take the free samples, about 41% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 327 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?


(b) What is the probability that fewer than 200 will take your free sample?


(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.41, while P(sample) = 0.64.


(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).