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1. Five males with a particular...

1. 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) 0.4182 0.3983 0.1517 0.0289 0.0028 0.0001

a. µ=___ (Round to one decimal place as needed

b. The table is not a probability distribution

2. Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.44. The table describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls?

x P(x)

0 0.176

1 0.414

2 0.325

3 0.085

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

a. µ=___ (Round to two decimal places as needed)

b. The table is not a probability distribution

3. Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable x is the number of Mexican-Americans on the jury.

x 0 1 2 3 4 5 6 7 8 9 10 11 12

P(x) 0.000 0.003 0.016 0.054 0.121 0.193 0.226 0.193 0.121 0.054 0.016 0.003 0.000

a. Find the probability of exactly 2 Mexican Americans among 12 jurors.

P(2)=___

4. Multiple-choice questions each have five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to three questions.

a. Use the multiplication rule to find P(CWW), where C denotes a correct answer and W denotes a wrong answer.

P(CWW)=___ (Type an exact answer)

5. Thirteen peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 13 offspring peas; no more than 1 has a green pod. Is it unusual to get no more than 1 pea with a green pod when 13 offspring peas are generated? Why or Why not?

The probability that no more than 1 of the 13 offspring peas has a green pod is___ (Round to three decimal places as needed)

6. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 10 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is___(Round to three decimal places as needed)

7. Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. use the given values of n and p to find the mean µ and standard deviation σ. Also, use the range rule of thumb to find the minimum usual value µ - 2σ and the maximum usual value µ + 2σ.

N= 1410, p=4/5

µ=___

8. Several psychology students are unprepared for a surprise true/false test with 10 questions, and all of their answers are guesses.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass by guessing and getting at least 7 correct answers? Why or Why not?

µ=___

9. A headline in a certain newspaper states that “most stay at first job less than 2 years. “That headline is based on an online poll of 340 college graduates. Among those polled, 77% stayed at their first full-time job less than 2 years. Complete parts (A) through (c)

a. Assume that 50% is the true percentage of graduates who stay at their first job less than two years, find the mean and standard deviation of the numbers of such graduates in randomly selected groups of 340 graduates.

The mean is ___ graduates

b. Assuming that the 50% rate in part (a) is correct, find the range of usual values for the numbers of graduates among 340 who stay at their first job less than two years

The numbers of graduates among 340 who stay at their first job less than two years should usually fall between ___ and___(Use ascending order. Round to one decimal place as needed)

c. Find the actual number of surveyed graduates who stayed at their first job less than two years. Use the range of values from part (b) to determine whether that number is XXXXX Does the result suggest that the headline is not justified?

The actual number of surveyed graduates who stayed at their first job less than two years is?__(Round to the nearest whole number as needed)

10. A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

Find the probability that a given class period runs between 51.25 and 51.5 minutes.___(Round to three decimal places as needed)

x 0 1 2 3 4 5

P(x) 0.4182 0.3983 0.1517 0.0289 0.0028 0.0001

a. µ=___ (Round to one decimal place as needed

b. The table is not a probability distribution

2. Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.44. The table describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls?

x P(x)

0 0.176

1 0.414

2 0.325

3 0.085

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

a. µ=___ (Round to two decimal places as needed)

b. The table is not a probability distribution

3. Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable x is the number of Mexican-Americans on the jury.

x 0 1 2 3 4 5 6 7 8 9 10 11 12

P(x) 0.000 0.003 0.016 0.054 0.121 0.193 0.226 0.193 0.121 0.054 0.016 0.003 0.000

a. Find the probability of exactly 2 Mexican Americans among 12 jurors.

P(2)=___

4. Multiple-choice questions each have five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to three questions.

a. Use the multiplication rule to find P(CWW), where C denotes a correct answer and W denotes a wrong answer.

P(CWW)=___ (Type an exact answer)

5. Thirteen peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 13 offspring peas; no more than 1 has a green pod. Is it unusual to get no more than 1 pea with a green pod when 13 offspring peas are generated? Why or Why not?

The probability that no more than 1 of the 13 offspring peas has a green pod is___ (Round to three decimal places as needed)

6. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 10 tablets, then accept the whole batch if there is only one or none that doesn’t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is___(Round to three decimal places as needed)

7. Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. use the given values of n and p to find the mean µ and standard deviation σ. Also, use the range rule of thumb to find the minimum usual value µ - 2σ and the maximum usual value µ + 2σ.

N= 1410, p=4/5

µ=___

8. Several psychology students are unprepared for a surprise true/false test with 10 questions, and all of their answers are guesses.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass by guessing and getting at least 7 correct answers? Why or Why not?

µ=___

9. A headline in a certain newspaper states that “most stay at first job less than 2 years. “That headline is based on an online poll of 340 college graduates. Among those polled, 77% stayed at their first full-time job less than 2 years. Complete parts (A) through (c)

a. Assume that 50% is the true percentage of graduates who stay at their first job less than two years, find the mean and standard deviation of the numbers of such graduates in randomly selected groups of 340 graduates.

The mean is ___ graduates

b. Assuming that the 50% rate in part (a) is correct, find the range of usual values for the numbers of graduates among 340 who stay at their first job less than two years

The numbers of graduates among 340 who stay at their first job less than two years should usually fall between ___ and___(Use ascending order. Round to one decimal place as needed)

c. Find the actual number of surveyed graduates who stayed at their first job less than two years. Use the range of values from part (b) to determine whether that number is XXXXX Does the result suggest that the headline is not justified?

The actual number of surveyed graduates who stayed at their first job less than two years is?__(Round to the nearest whole number as needed)

10. A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

Find the probability that a given class period runs between 51.25 and 51.5 minutes.___(Round to three decimal places as needed)

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