Question 1

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-The Poisson probability distribution is used with
A)a continuous random variable
B)a discrete random variable
C)either a continuous or discrete random variable
D)any random variable

Accepted Answer

The Poisson distribution is used with a discrete random variable, which is appropriate for counting the number of fish Pete catches in a day.

Question 2

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is
A).008
B).096
C).104
D).8

Accepted Answer

The probability of catching fish on exactly one day can be calculated using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n=3, k=1, and p=0.8. This results in 3 * 0.8^1 * 0.2^2 = 0.096.

Question 3

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Excel's POISSON.DIST function has how many inputs?
A)2
B)3
C)4
D)5

Accepted Answer

The POISSON.DIST function in Excel has 3 inputs: x (the actual value), mean (the expected value), and cumulative (a logical value that determines whether the function returns the cumulative distribution function or the probability density function).

Question 4

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Refer to Exhibit 5-10. The expected number of days Pete will catch fish is
A).6
B).8
C)2.4
D)3

Accepted Answer

The expected value can be calculated by multiplying the probability of catching fish (0.8) by the number of days (3) Pete goes fishing.

E(X) = 0.8 * 3 = 2.4

Therefore, the expected number of days Pete will catch fish is 2.4. Option C is the correct answer.

Question 5

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is
A).008
B).096
C).104
D).8

Accepted Answer

We can use the binomial distribution formula to calculate the probability of at most one success in three independent trials with probability of success 0.8. P(X ≤ 1) = P(X = 0) + P(X = 1) = (0.2)^3 + 3(0.8)(0.2)^2 = 0.008 + 0.096 = 0.104. Therefore, the correct answer is (C).

Question 6

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-The Poisson probability distribution is a
A)continuous probability distribution
B)discrete probability distribution
C)uniform probability distribution
D)normal probability distribution

Accepted Answer

The Poisson probability distribution is a type of discrete probability distribution that models the number of rare events that occur within a fixed interval of time or space. In this case, we are interested in the number of days out of three that Pete catches fish, so the Poisson distribution is appropriate.

Question 7

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
-Refer to Exhibit 5-9. The probability that there are no females in the sample is
A)0.0778
B)0.7780
C)0.5000
D)0.3456

Accepted Answer

The probability of selecting a female voter in the sample is 0.4, and the probability of selecting a male voter is 0.6. The probability of selecting no females in the sample is therefore (0.6)^5, which is approximately 0.0778.

Question 8

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
-Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is
A)0.0778
B)0.7780
C)0.5000
D)0.3456

Accepted Answer

The probability of selecting a female voter from the population is 0.4, and the probability of selecting a male voter is 0.6. The probability of selecting exactly 2 female voters in a sample of 5 can be calculated using the binomial probability formula:
P(2 female voters) = (5 choose 2) * (0.4)^2 * (0.6)^3
= 10 * 0.16 * 0.216
= 0.3456
Therefore, the answer is choice D.

Question 9

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is
A).16
B).48
C).8
D)2.4

Accepted Answer

Let X be the number of days that Pete catches fish in a week. Then X follows a binomial distribution with parameters n = 3 (number of trials) and p = 0.8 (probability of success on each trial).

The variance of a binomial distribution is Var(X) = np(1-p).

Substituting n = 3 and p = 0.8, we get Var(X) = 3(0.8)(1-0.8) = 0.48.

Therefore, the variance of the number of days Pete will catch fish is 0.48.

Hence, the correct answer is B.

Question 10

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Excel's POISSON.DIST function can be used to compute
A)bin width for histograms
B)Poisson probabilities
C)cumulative Poisson probabilities
D)Both Poisson probabilities and cumulative Poisson probabilities are correct.

Accepted Answer

Excel's POISSON.DIST function can compute both Poisson probabilities and cumulative Poisson probabilities.

Question 11

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-When dealing with the number of occurrences of an event over a specified interval of time or space and when the occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval, the appropriate probability distribution is a
A)binomial distribution
B)Poisson distribution
C)normal distribution
D)hypergeometric probability distribution

Accepted Answer

This scenario describes the characteristics of a Poisson distribution, where the occurrence of events is random and independent of previous occurrences, and the rate of occurrence is constant over the specified interval of time or space.

Question 12

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?
A)0.0896
B)0.2936
C)0.0413
D)0.0007

Accepted Answer

The answer of Exhibit 5-8
The student body of a large...

Question 13

Exhibit 5-11
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-11. The random variable x satisfies which of the following probability distributions?
A)normal
B)Poisson
C)binomial
D)Not enough information is given to answer this question.

Accepted Answer

The given information implies that the random variable x follows a Poisson distribution, where the mean and variance are equal to 5.3. The Poisson distribution is used to model the number of occurrences of rare events in a fixed interval of time or space.

Question 14

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-When using Excel's POISSON.DIST function, one should choose TRUE for the third input if
A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Accepted Answer

The third input of the POISSON.DIST function specifies whether a cumulative probability (TRUE) or a single probability (FALSE) is desired. Since Pete is going fishing for three days, we want to know the probability that he catches fish on at least one of those days, which is a cumulative probability. Therefore, we should choose TRUE for the third input.

Question 15

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-8. What is the random variable in this experiment?
A)the 60% of female students
B)the random sample of 8 students
C)the number of female students out of 8
D)the student body size

Accepted Answer

The random variable in this experiment is the number of female students out of the 8 randomly selected students.

Question 16

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?
A)0.0413
B)0.0079
C)0.0007
D)0.0499

Accepted Answer

The answer of Exhibit 5-8
The student body of a large...

Question 17

Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
-Refer to Exhibit 5-9. What is the random variable in this experiment?
A)the 40% of female registered voters
B)the random sample of 5 voters
C)the number of female voters out of 5
D)the number of registered voters in the nation

Accepted Answer

The random variable in this experiment is the number of female voters out of 5 selected. This is because we are interested in counting the number of female voters in the sample of 5 that we have selected. A and D are incorrect because they are not random variables in this specific experiment. B is not the random variable because it is the process of selecting the voters, not the outcome we are interested in.

Question 18

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the
A)normal distribution
B)binomial distribution
C)Poisson distribution
D)uniform distribution

Accepted Answer

The Poisson distribution is most appropriate for situations where the occurrence of a particular event is rare, but there are many opportunities for the event to occur. In the case of blemishes or flaws occurring in each 100 feet of material, the occurrence of a flaw is relatively rare, but there are many opportunities for flaws to occur. Therefore, the Poisson distribution is the most appropriate choice.

Question 19

Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 7 are female?
A)0.1064
B)0.0896
C)0.0168
D)0.8936

Accepted Answer

The probability of selecting at least 7 female students out of a sample of 8 students from a population where 60% are female is 0.1064. This can be calculated using the binomial distribution formula:P(X >= 7) = 1 - P(X < 7) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)) = 1 - (0.0039 + 0.0234 + 0.0702 + 0.1404 + 0.1966 + 0.2168 + 0.1966) = 0.1064

Question 20

Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.
-Refer to Exhibit 5-10. What is the random variable in this experiment?
A)the 0.8 probability of catching fish
B)the 3 days
C)the number of days out of 3 that Pete catches fish
D)the number of fish in the body of water

Accepted Answer

The random variable in this experiment is the number of days out of 3 that Pete catches fish. This is because it is the variable that is being measured and can take on different values, specifically 0, 1, 2, or 3. The probability of catching fish (0.8) is not the random variable as it is a fixed probability. The number of days (3) is not the random variable as it is constant and does not vary. The number of fish in the body of water is not being measured or varied in this experiment, so it is not the random variable.

Quiz 5: Discrete Probability Distributions

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -The Poisson probability distribution is used with

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Excel's POISSON.DIST function has how many inputs?

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Refer to Exhibit 5-10. The expected number of days Pete will catch fish is

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -The Poisson probability distribution is a

Exhibit 5-9 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. -Refer to Exhibit 5-9. The probability that there are no females in the sample is

Exhibit 5-9 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. -Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Excel's POISSON.DIST function can be used to compute

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -When using Excel's POISSON.DIST function, one should choose TRUE for the third input if

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-8. What is the random variable in this experiment?

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?

Exhibit 5-9 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. -Refer to Exhibit 5-9. What is the random variable in this experiment?

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 7 are female?

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. -Refer to Exhibit 5-10. What is the random variable in this experiment?