Based on long experience, an airline found that about 4% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 270 ticket reservations for an airplane with only 255 seats. (Round your answers to four decimal places.)

(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 270 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation?

P(r ≥ 270)P(r ≥ 255)    P(r ≤ 270)P(r ≤ 255)

(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation?

Linda is a sales associate at a large auto dealership. At her commission rate of 25% of gross profit on each vehicle she sells, Linda expects to earn 310 for each car sold and 390 for each truck or SUV sold. Linda motivates herself by using probability estimates of her sales. For a sunny Saturday in April, she estimates her car sales as follows:

Linda's estimate of her truck or SUV sales is

5. Lindas best estimate of her earnings for the day.

6. the variance of the number of cars Linda sells for the day.

7. the variance of the number of trucks or SUVs Linda sells for the day.

8. the variance of Linda's earnings for the day.

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.

a. What is the probability that more than 830 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions?

b. What is the probability that fewer than 1,030 consumers claim that quality of product is an influence in their buying decisions?

c. What is the probability that between 82% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions?

Part V. 1. Events G and H are defined on the sample space. If P(G) = 0.3, P(H) = 0.2, and P(G ! H) = 0.1 a) Are G and H independent? Explain. __________________________________________________________________________ b) Are G and H mutually exclusive? Explain. ___________________________________________________________________________ 2. The classical probability concept applies only when all possible outcomes are ______________________. 5 3. If A is the event that I win the lottery and B is the event that I go on vacation, then P(B | A) can be described in words as the probability that ______________________________________________________________. 4. A restaurant menu has 8 main courses, 5 appetizers, 6 desserts, and 4 beverages. The number of ways that a patron can select a meal with one appetizer, one main course, one dessert and one beverage is ________________________________________________. 5. The number of 5-player basketball teams that can be formed from a group of 11 players is _______________________________________________. 6. How many ways can letters of PROBABILITY be arranged? _____________________________________________.

Before a long road trip alone, I put 13 chocolate chunk cookies and 9 snickerdoodles in a bag for snacks. After one hour of driving, you reach in the bag without looking and take out a cookie at random and eat it. After another hour, you take out another cookie (again randomly, without looking). Show the work!

1. Show the probability tree summarizing the probabilities of possible outcome of taking cookies out of the bag (this is two trial without replacement).

2. Use the tree to construct a discrete probability distribution for the number of chocolate chunk cookies I take out of the bag.

3. From the discrete probability distribution you constructed in #2, calculate the mean and standard deviation of the number of chocolate chunk cookies I take out of the bag (remember, because we’re looking at probabilities, mean and standard deviation have to be calculated differently than in the context of a numeric variable).

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,200 consumers is taken and each is asked which of these three factors influence their buying decisions.

a. What is the probability that more than 920 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions?
b. What is the probability that fewer than 1,125 consumers claim that quality of product is an influence in their buying decisions?
c. What is the probability that between 81% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions?

A study on aggressive driving found that 45 % of drivers say that they have yelled at another driver. A random sample of 280 drivers in Halifax is selected and are asked whether they have yelled at other drivers.

1. What is the distribution of the number of sampled drivers who will say ”yes”, they have yelled at another driver? State only the name of the distribution.

2. What are the mean and standard deviation of the number of sampled drivers who will say "yes"?

The mean:

The standard deviation (Round to three decimals):

3. What is the probability that at least 135 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

4. What is the probability that at most 131 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

5. Use the normal approximation to calculate the probability that there will be exactly 131 sampled drivers who will say yes. [Hint: use normal approximation]

Based on long experience, an airline found that about 8% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats.

(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation?

P(r ≥ 255)P(r ≥ 267)    P(r ≤ 255)P(r ≤ 267)

(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)

There are 35 identically sized balls in a box, where 5 of each of the colors are present: red, orange, yellow, green, blue, indigo, and violet. Justify your answer for each.

a. Suppose you draw a sample of seven balls without replacement from the box. What is the probability that the sample contains balls of exactly two colors? (for example, the event for which you have 4 red and 3 blue would satisfy)

b. Suppose you draw a sample of seven balls with replacement from the box (you draw one, then replace, draw one, then replace, and so on). What is the probability that the sample contains balls of exactly two colors?

c. Suppose you draw a sample of three balls without replacement. Define ? to be the random variable on the number of red balls in the sample and ? the random variable on the number of orange balls in the sample. Find the joint probability distribution function ??,?(?, ?) for the random variables ? and

Sam is a representative who sells large appliances such as refrigerators, stoves, and so forth. Let x be the number of appliances Sam sells on a given day. And let f be the number of days (frequency) with which he sells x appliances. For a random sample of 240 days, Sam had the following sales record

x 1 2 3 4 5 6 7

f 14 72 ? 41 28 14 8

Assume the sales record is representative of the population of all sales days: (a) Use relative frequency to find P(x) for each x from 0 to 7. (b) Use a histogram to graph the probability distribution of part (a). (c) Compute the probability that x is between 2 and 5 (including 2 and 5). (d) Compute the probability that x is less than 3. (e) Compute the expected value of the x distribution. (f) NOT REQUIRED (longer question) Compute the standard deviation of the x distribution.