A test is designed to detect cancer. If a person has cnacer, then the probability that the test will detect it is .95; if the person does not have cancer, the probability that the test will erroneously indicate that he does have cancer is .1. Assume 15% of the population who take the test have cancer. What is t he probability that a person described by the test as not having cancer really does have it?

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)

(a)    2


(b)    5


(c)    6

Suppose that the probability that a passenger will miss a flight is 0.0976. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of 59 passengers.

​(a) If 61 tickets are​ sold, what is the probability that 60 or 61 passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that 65 tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of 58 ​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 5​%?

The ABC Co. is considering a new consumer product. They believe there is a probability of 0.30 that the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $45,000; if they add an assembly line and XYZ does follow, they still expect a $12,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $450,000; if XYZ does compete for this market, ABC expects a loss of $80,000. If ABC does nothing, XYZ does nothing. (a) Determine the EMV of each decision. (b) Determine the EOL of each decision. (c) Compare the results of (a) and (b). (d) Calculate the EVPI

Prove that the Poisson distribution is in the exponential family of probability distributions given that the Poisson parameter is positive

The population proportion is 0.40. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? (Round your answers to 4 decimal places.)

(a) n = 100

(b) n = 200

(c) n = 500

(d) n = 1,000

(e) What is the advantage of a larger sample size?

We can guarantee p will be within ±0.04 of the population proportion p.

There is a higher probability σp will be within ±0.04 of the population standard deviation.

As sample size increases, E(p) approaches p.

There is a higher probability p will be within ±0.04 of the population proportion p.

Suppose that the probability that a passenger will miss a flight is .0946. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of 56 passengers.

​(a) If 58 tickets are​ sold, what is the probability that 57 or 58 passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that 62 tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of 51 ​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 5​%?

Suppose that the probability that a passenger will miss a flight is 0.0917. Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be "bumped" from the flight. Suppose that an airplane has a seating capacity of 51 passengers.

​(a) If 53 tickets are​ sold, what is the probability that 52 or 53 passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that 57 tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of 61 passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below 5​%?

It is important to keep the probability of making Type I equal to α. With a t test, how do we keep the probability of Type I error in check?

What is the probability of randomly selecting a woman with green eyes and a man with children, P(green-eyed woman and a man with children)?

          WOMEN                      EYE COLOR               CHILDREN

                18                            Brown                                No

                22                            Brown                               Yes

                09                            Blue                                   No

                21                            Blue                                  Yes

                12                            Green                                No

                18                            Green                               Yes

            MEN                            EYE COLOR               CHILDREN

                24                            Brown                                No

                16                            Brown                               Yes

                12                            Blue                                   No

                18                            Blue                                  Yes

                10                            Green                                No

                20                            Green                               Yes