The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?	Number of girls x	P(x)
0	0.125
1	0.375
2	0.375
3	0.125

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Part 1

Choose the correct answer below.

A.

The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are not numerical.

B.

The random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are not numerical.

C.

The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are numerical.

D.

The random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are numerical.

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation.

x	0	1	2	3	4	5
P(x)	0.0010	0.0146	0.0879	0.2637	0.3955	0.2373

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Part 1

Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

=enter your response here

(Round to one decimal place as needed.)

B.

The table is not a probability distribution.

Part 2

Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

=enter your response here

(Round to one decimal place as needed.)

B.

The table is not a probability distribution.

Based on data from a car bumper sticker study, when a car is randomly selected, the number of bumper stickers and the corresponding probabilities are as shown below.

Complete parts (a) through (d).

x	P(x)
0	0.809
1	0.081
2	0.038
3	0.021
4	0.015
5	0.012
6	0.009
7	0.007
8	0.006
9

Click the icon to view the data table.

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Part 1

a. Does the given information describe a probability distribution?

Yes

No

Part 2

b. Assuming that a probability distribution is described, find its mean and standard deviation.

The mean is

enter your response here.

(Round to the nearest tenth as needed.)

Part 3

The standard deviation is

enter your response here.

(Round to the nearest tenth as needed.)

Part 4

c. Use the range rule of thumb to identify the range of values for usual numbers of bumper stickers.

The maximum usual value is

enter your response here.

(Round to the nearest tenth as needed.)

Part 5

The minimum usual value is

enter your response here.

(Round to the nearest tenth as needed.)

Part 6

d. Is it unusual for a car to have more than one bumper sticker? Explain.

A.

No, because the probability of having 1 bumper sticker is

0.081,

which is greater than 0.05.

B.

No, because the probability of more than 1 bumper sticker is

0.110,

which is greater than 0.05.

C.

Yes, because the probabilities for random variable x from 2 to 9 are all less than 0.05.

D.

Not enough information is given.

A Gallup poll of 1236 adults showed that 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without replacement, the events are not independent. Can the probability be found by using the binomial probability formula? Why or why not?

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Part 1

Choose the correct answer below.

A.

No. The selections are not independent, and the 5% guideline is not met.

B.

No. The selections are not independent.

C.

Yes. Although the selections are not independent, they can be treated as being independent by applying the 5% guideline.

D.

Yes. There are a fixed number of selections that are independent, can be classified into two categories, and the probability of success remains the same.

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied.

Randomlyselecting50adultsandaskingiftheylikerapmusic,recordingYes orNo

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Part 1

Choose the correct answer below.

A.

Yes,becauseall4requirementsaresatisfied.

B.

No, because the probability of success does not remain the same in all trials.

C.

No,becausetherearemorethantwopossibleoutcomes.

D.

No, because there are more than two possible outcomes and the trials are not independent.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.

Five cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded.

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Part 1

Does the probability experiment represent a binomial experiment?

A.

No, because there are more than two mutually exclusive outcomes for each trial.

B.

No, because the experiment is not performed a fixed number of times.

C.

Yes, because the experiment satisfies all the criteria for a binomial experiment.

D.

No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

Assume that a procedure yields a binomial distribution with

n=5

trials and a probability of success of

p=0.40.

Use a binomial probability table to find the probability that the number of successes x is exactly

2.

Part 1

P(2)=enter your response here

(Round to three decimal places as needed.)

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

n=19,

x=4,

p=0.15

A candy company claims that 12% of its plain candies are orange, and a sample of 200 such candies is randomly selected.

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Part 1

a. Find the mean and standard deviation for the number of orange candies in such groups of

200.

=enter your response here

(Do not round.)

Part 2

=enter your response here

(Round to one decimal place as needed.)

Part 3

b. A random sample of

200

candies contains

6

orange candies. Is this result unusual? Does it seem that the claimed rate of

12%

is wrong?

A.

Yes,because6isbelowtheminimumusualvalue.

Thus, the claimed rate of

12%

is

probably

wrong.

B.

Yes, because

6

is within the range of usual values. Thus, the claimed rate of

12%

is probably wrong.

C.

No,because6iswithintherangeofusualvalues.

Thus, the claimed rate of

12%

is

probably

wrong.

D.

Yes,because6isgreaterthanthemaximumusualvalue.

Thus, the claimed rate of

12%

is

notnecessarily

wrong.

Last year, a person wrote

132

checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance?

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Part 1

The mean number of checks written per day is

enter your response here.

(Round to three decimal places as needed.)

Part 2

The standard deviation is

enter your response here.

(Round to three decimal places as needed.)

Part 3

The variance is

enter your response here.

(Round to three decimal places as needed.)

A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had

12,732

children.

a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of

12,732

children.

b. Using the unrounded mean from part

(a),

find the probability that the number of tumor cases in a group of

12,732

children is 0 or 1.

c. What is the probability of more than one case?

d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?

Question content area bottom

Part 1

a. The mean number of cases is

enter your response here.

(Type an integer or decimal rounded to three decimal places as needed.)

Part 2

b. The probability that the number of cases is exactly 0 or 1 is

enter your response here.

(Round to three decimal places as needed.)

Part 3

c. The probability of more than one case is

enter your response here.

(Round to three decimal places as needed.)

Part 4

d. Let a probability of 0.05 or less be "very small," and let a probability of 0.95 or more be "very large". Does the cluster of four cases appear to be attributable to random chance? Why or why not?

A Yes, because the probability of more than one case is very large.

B.

No, because the probability of more than one case is very large.

C.

Yes, because the probability of more than one case is very small.

D.

No, because the probability of more than one case is very small.