# Answer to Question #36590 in Statistics and Probability for Mona7Berlin 1

Question #36590

Gestation Periods. The probability is 0.314 that the gestation

period of a woman will exceed 9 months. In six human

births, what is the probability that the number in which the gestation

period exceeds 9 months is

a. exactly three?

b. exactly five?

c. at least five?

d. between three and five, inclusive?

Recidivism. In the Scientific American article “Reducing

Crime: Rehabilitation is Making a Comeback,” R. Doyle examined

rehabilitation of felons. One aspect of the article discussed

recidivism of juvenile prisoners between 14 and 17 years old, indicating

that 82% of those released in 1994 were rearrested within

3 years. Suppose that, today, six newly released juvenile prisoners

between 14 and 17 years old are selected at random.

a. Assuming that the recidivism rate is the same today as it was

in 1994, determine the probability distribution for the number,

Y , who are rearrested within 3 years.

b. Determine and interpret the mean of Y .

c. If, in fact, exactly two of the six newly released juvenile prisoners

are rearrested within 3 years, would you be inclined to

conclude that the recidivism rate today has decreased from the

82% rate in 1994? Explain your reasoning. Hint: First consider

the probability P(Y = 2).

d. If, in fact, exactly four of the six newly released juvenile prisoners

are rearrested within 3 years, would you be inclined to

conclude that the recidivism rate today has decreased from the

82% rate in 1994? Explain your reasoning.

Lotto. A previous Arizona state lottery called Lotto is

played as follows: The player selects six numbers from the numbers

1–42 and buys a ticket for $1. There are six winning numbers,

which are selected at random from the numbers 1–42. To

win a prize, a Lotto ticket must contain three or more of the winning

numbers. A probability distribution for the number of winning

numbers for a single ticket is shown in the following table.

Number of

winning numbers Probability

0 0.3713060

1 0.4311941

2 0.1684352

3 0.0272219

4 0.0018014

5 0.0000412

6 0.0000002

a. If you buy one Lotto ticket, determine the probability that you

win a prize. Round your answer to three decimal places.

b. If you buy one Lotto ticket per week for a year, determine the

probability that you win a prize at least once in the 52 tries.

period of a woman will exceed 9 months. In six human

births, what is the probability that the number in which the gestation

period exceeds 9 months is

a. exactly three?

b. exactly five?

c. at least five?

d. between three and five, inclusive?

Recidivism. In the Scientific American article “Reducing

Crime: Rehabilitation is Making a Comeback,” R. Doyle examined

rehabilitation of felons. One aspect of the article discussed

recidivism of juvenile prisoners between 14 and 17 years old, indicating

that 82% of those released in 1994 were rearrested within

3 years. Suppose that, today, six newly released juvenile prisoners

between 14 and 17 years old are selected at random.

a. Assuming that the recidivism rate is the same today as it was

in 1994, determine the probability distribution for the number,

Y , who are rearrested within 3 years.

b. Determine and interpret the mean of Y .

c. If, in fact, exactly two of the six newly released juvenile prisoners

are rearrested within 3 years, would you be inclined to

conclude that the recidivism rate today has decreased from the

82% rate in 1994? Explain your reasoning. Hint: First consider

the probability P(Y = 2).

d. If, in fact, exactly four of the six newly released juvenile prisoners

are rearrested within 3 years, would you be inclined to

conclude that the recidivism rate today has decreased from the

82% rate in 1994? Explain your reasoning.

Lotto. A previous Arizona state lottery called Lotto is

played as follows: The player selects six numbers from the numbers

1–42 and buys a ticket for $1. There are six winning numbers,

which are selected at random from the numbers 1–42. To

win a prize, a Lotto ticket must contain three or more of the winning

numbers. A probability distribution for the number of winning

numbers for a single ticket is shown in the following table.

Number of

winning numbers Probability

0 0.3713060

1 0.4311941

2 0.1684352

3 0.0272219

4 0.0018014

5 0.0000412

6 0.0000002

a. If you buy one Lotto ticket, determine the probability that you

win a prize. Round your answer to three decimal places.

b. If you buy one Lotto ticket per week for a year, determine the

probability that you win a prize at least once in the 52 tries.

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