# Statistics 2

Statistics 2

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Question 1

According to a survey of American households, the probability that the residents own 2 cars is 80%, given annual income is over \$25,000.

Of the households surveyed, 60% had incomes over \$25,000; 70% owned 2 cars.

What is the probability that the residents of a household own 2 cars AND have an annual income over \$25,000?

0.12

0.18

0.48

0.22

Question 2

If two events are collectively exhaustive, what is the probability that both occur at the same time?

0.50.

1.00.

Cannot be determined from the information given.

Question 3

Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.

Referring to TABLE 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol?

20/30 or 66.67%

20/50 or 40%

20/170 or 11.77%

20/400 or 5%

Question 4 text

If two events are mutually exclusive, what is the probability that both occur at the same time?

0.50.

1.00.

Cannot be determined from the information given.

Question 5

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is:

0.20

0.32

0.40

0.88

Question 6

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?

0.078

0.1175

0.156

0.310

Question 7

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

0.06

0.50

0.92

0.94

Question 8

Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.

Referring to TABLE 4-1, what proportion of accidents involved more than one vehicle?

50/400 or 12.5%

75/400 or 18.75%

275/400 or 68.75%

325/400 or 81.25%

Question 9

Suppose that a judge’s decisions follow a binomial distribution and that his verdict is correct 90% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

True

False

Question 10

The local police department must write an average of 5 traffic tickets each day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

The number of tickets written is 6.5 each day.

Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.

If we sampled all days, the expected number of tickets written would be 6.5 tickets per day.

The mean cannot be interpreted since you can write 0.5 tickets.

Question 11

The Poisson distribution can be used to model a continuous random variable.

True

False

Question 12

The diameters of 10 randomly selected bolts have a binomial distribution.

True

False

Question 13

The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

True

False

Question 14

Whenever p = 0.1 and n is small, the binomial distribution will be

symmetric.

right-skewed.

left-skewed.

None of the above.

Question 15

A lab orders 100 rats per week for each of the 52 weeks in the year. Suppose the mean cost of rats is \$13.00 per week. Interpret this value.

Most of the weeks resulted in rat costs of \$13.00.

The median cost for the rats is \$13.00.

The expected weekly cost for all rat purchases is \$13.00.

The rat cost that occurs more often than any other is \$13.00.

Question 16

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

True

False

Question 17

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight.

Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established?

1.56 pounds

4.84 pounds

5.20 pounds

7.36 pounds

Question 18

Which of the following about the normal distribution is NOT true?

Theoretically, the mean, median, and mode are the same.

About 2/3 of the observations fall within ± 1 standard deviation from the mean.

It is a discrete probability distribution.

Its parameters are the mean, µ (mu), and standard deviation, ó (sigma).

Question 19

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?

0.0668

0.0245

0.1280

1.2045

Question 20

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

0.3551

0.3085

0.2674

0.1915

Question 21

The probability that a standard normal random variable, Z, falls between -2.00 and -0.44 is 0.6472.

True

Flase

Question 22

The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between – 2.10 and – 1.50.

True

False

Question 23

Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there. One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease. Scientists have calculated that the average diameter of the diseased trees is 42 centimeters. They also know that approximately 95% of the diameters fall between 32 and 52 centimeters and almost all of the diseased trees has diameters between 27 and 57 centimeters. When modeling the diameters of diseased trees, which distribution should the scientists use?

Poisson distribution

Binomial distribution

Normal distribution

Cumulative distribution

Question 24

The probability that a standard normal random variable, Z, is less than 50 is approximately 0.

True

False

Question 25

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is _______?

0.1253

0.1056

0.0124

0.2145

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