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Answer on Statistics and Probability Question 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.
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