7. The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once t

[answerhappygod]

7. The one-time fling! Have you ever purchased an article of
clothing (dress, sports jacket, etc.), worn the
item once to a party, and then returned the
purchase? This is called a one-time fling.
About 15% of all adults deliberately do a one-time fling and feel
no guilt about it! In a group of ten adult friends, what is the
probability of the following? (Round your answers to three decimal
places.)
(a) no one has done a one-time fling


(b) at least one person has done a one-time fling


(c) no more than two people have done a one-time fling
13. Do you tailgate the car in front of you? About 30% of all
drivers will tailgate before passing, thinking they can make the
car in front of them go faster. Suppose that you are driving a
considerable distance on a two-lane highway and are passed by 10
vehicles.
(a) Let r be the number of vehicles that
tailgate before passing. Make a histogram showing the probability
distribution of r for r = 0
through r = 10.
(b) Compute the expected number of vehicles out of 10 that will
tailgate. vehicles

(c) Compute the standard deviation of this distribution. (Round
your answer to two decimal places.) vehicles
14. The Denver Post reported that, on
average, a large shopping center had an incident of shoplifting
caught by security 2.2 times every six hours. The shopping center
is open from 10 A.M. to 9 P.M. (11 hours).
Let r be the number of shoplifting incidents
caught by security in an 11-hour period during which the center is
open.
(a) Explain why the Poisson probability distribution would be a
good choice for the random variable r.
Frequency of shoplifting is a rare
occurrence. It is reasonable to assume the events are
independent.
Frequency of shoplifting is a common
occurrence. It is reasonable to assume the events are
independent.
Frequency of shoplifting is a common
occurrence. It is reasonable to assume the events are
dependent.
Frequency of shoplifting is a rare
occurrence. It is reasonable to assume the events are
dependent.
What is 𝜆? (Round your answer to three decimal places.)

(b) What is the probability that from 10 A.M. to 9 P.M. there will
be at least one shoplifting incident caught by security? (Round
your answer to four decimal places.)


(c) What is the probability that from 10 A.M. to 9 P.M. there will
be at least three shoplifting incidents caught by security? (Round
your answer to four decimal places.)


(d) What is the probability that from 10 A.M. to 9 P.M. there will
be no shoplifting incidents caught by security? (Round your answer
to four decimal places.)
15. USA Today reported that Parkfield, California, is
dubbed the world's earthquake capital because it sits on top of the
notorious San Andreas fault. Since 1857, Parkfield has had a major
earthquake on the average of 1.4 times every 22 years.
(a) Explain why a Poisson probability distribution would be a
good choice for r = number of earthquakes in a
given time interval.
Frequency of earthquakes is a common occurrence. It is
reasonable to assume the events are dependent.
Frequency of earthquakes is a rare occurrence. It is reasonable
to assume the events are dependent.
Frequency of earthquakes is a common occurrence. It is
reasonable to assume the events are independent.
Frequency of earthquakes is a rare occurrence. It is reasonable
to assume the events are independent.
(b) Compute the probability of at least one major earthquake in the
next 22 years. Round 𝜆 to the nearest hundredth, and use a
calculator. (Use 4 decimal places.)


(c) Compute the probability that there will be no major earthquake
in the next 22 years. Round 𝜆 to the nearest hundredth, and use a
calculator. (Use 4 decimal places.)

(d) Compute the probability of at least one major earthquake in the
next 47 years. Round 𝜆 to the nearest hundredth, and use a
calculator. (Use 4 decimal places.)


(e) Compute the probability of no major earthquakes in the next 47
years. Round 𝜆 to the nearest hundredth, and use a calculator. (Use
4 decimal places.)