The National Institute of Mental Health reports that there i

The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Suppose that four randomly selected adult Americans are examined for psychiatric disorders. Binomial probabilities are shown in the table below:

Find the probability that at least two people have a psychiatric disorder. Round off to the nearest whole percent.

Select one:

A. 3%

B. 15%

C. 18%

D. 59%

E. None of the above.

Question 2

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From the table in Question 1: Find the probability that exactly two people have a psychiatric disorder. Round off to the nearest whole percent.

Select one:

A. 3%

B. 15%

C. 18%

D. 59%

E. None of the above.

Question 3

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The owner of a fast-food restaurant knows that the number of cars using the drive-through window between 3:00 and 3:15 pm has a Poisson distribution with lambda equal to 2.4. Poisson probabilites are given in the table below:

Find the probability that more than two cars use the drive-through window. Round off to the nearest whole percent.

Select one:

A. 26%

B. 56%

C. 43%

D. 21%

E. None of the above.

Question 4

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From the table in Question 3: Find the probability that at least four cars use the drive-through window. Round off to the nearest whole percent.

Select one:

A. 13%

B. 78%

C. 90%

D. 22%

E. None of the above.

Question 5

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Which one of the statements below is most likely to be included in an exam question about the binomial probability distribution? [See page 195 to review properties of the binomial distribution.]

Select one:

A. A sports car dealer surcharges from 5% to 7% for the most popular colors, such as red and silver.

B. Ornithologists classify bird species as either capable of flight, or flightless. Penguins, kiwis, rheas, ostriches, emus, and cassowaries are all flightless, but no one is sure what percentage of all birds these represent.

C. The later at night it gets, the greater the probability of your being involved in an alcohol-related auto accident.

D. Approximately 10% of all Christmas presents bought in stores are returned by the recipients.

E. On Admiralty Island in Glacier Bay National Park, the population density for brown bears is approximately one bear per square mile.

X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
0	0.4096	0.4096	0	0.5904	1
1	0.4096	0.8192	0.4096	0.1808	0.5904
2	0.1536	0.9728	0.8192	0.0272	0.1808
3	0.0256	0.9984	0.9728	0.0016	0.0272
4	0.0016	1	0.9984	0	0.0016

Solution

The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Suppose that four randomly selected adult Americans are examined for psychiatric disorders. Binomial probabilities are shown in the table below:

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.4096

0.4096

0

0.5904

1

1

0.4096

0.8192

0.4096

0.1808

0.5904

2

0.1536

0.9728

0.8192

0.0272

0.1808

3

0.0256

0.9984

0.9728

0.0016

0.0272

4

0.0016

1

0.9984

0

0.0016

Find the probability that at least two people have a psychiatric disorder. Round off to the nearest whole percent.

Select one:

A. 3%

B. 15%

C. 18%

D. 59%

E. None of the above.

Question 2

Not yet answered

Points out of 1

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From the table in Question 1: Find the probability that exactly two people have a psychiatric disorder. Round off to the nearest whole percent.

Select one:

A. 3%

B. 15%

C. 18%

D. 59%

E. None of the above.

Question 3

Not yet answered

Points out of 1

Flag question

Question text

The owner of a fast-food restaurant knows that the number of cars using the drive-through window between 3:00 and 3:15 pm has a Poisson distribution with lambda equal to 2.4. Poisson probabilites are given in the table below:

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.0907

0.0907

0.0000

0.9093

1.0

1

0.2177

0.3084

0.0907

0.6916

0.9093

2

0.2613

0.5697

0.3084

0.4303

0.6916

3

0.2090

0.7787

0.5697

0.2213

0.4303

4

0.1254

0.9041

0.7787

0.0959

0.2213

5

0.0602

0.9643

0.9041

0.0357

0.0959

Find the probability that more than two cars use the drive-through window. Round off to the nearest whole percent.

Select one:

A. 26%

B. 56%

C. 43%

D. 21%

E. None of the above.

Question 4

Not yet answered

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From the table in Question 3: Find the probability that at least four cars use the drive-through window. Round off to the nearest whole percent.

Select one:

A. 13%

B. 78%

C. 90%

D. 22%

E. None of the above.

Question 5

Not yet answered

Points out of 1

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Question text

Which one of the statements below is most likely to be included in an exam question about the binomial probability distribution? [See page 195 to review properties of the binomial distribution.]

Select one:

A. A sports car dealer surcharges from 5% to 7% for the most popular colors, such as red and silver.

B. Ornithologists classify bird species as either capable of flight, or flightless. Penguins, kiwis, rheas, ostriches, emus, and cassowaries are all flightless, but no one is sure what percentage of all birds these represent.

C. The later at night it gets, the greater the probability of your being involved in an alcohol-related auto accident.

D. Approximately 10% of all Christmas presents bought in stores are returned by the recipients.

E. On Admiralty Island in Glacier Bay National Park, the population density for brown bears is approximately one bear per square mile.

X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
0	0.4096	0.4096	0	0.5904	1
1	0.4096	0.8192	0.4096	0.1808	0.5904
2	0.1536	0.9728	0.8192	0.0272	0.1808
3	0.0256	0.9984	0.9728	0.0016	0.0272
4	0.0016	1	0.9984	0	0.0016