Answer:
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In a national survey college students were asked, "How often do you wear a seat belt when riding in a car driven by someone else?" The response frequencies appear in the table to the right. (a) Construct a probability model for seat-belt use by a passenger. (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else?
Response , Frequency
Never 102
Rarely 319
Sometimes 524
Most of the time 1067
Always 2727
n= 102+319+524+1067+2727= 4739
(a) Complete the table below.
Response
Probability To calculate the probability for each response you have to divide the frequency of each category by the total of people surveyed:
Never P(N)= 102/4739= 0.0215
(Round to the nearest thousandth as needed.)
Rarely P(R)= 319/4739= 0.0673
(Round to the nearest thousandth as needed.)
Sometimes P(S)= 524/4739= 0.1106
(Round to the nearest thousandth as needed.)
Most of the time P(M)= 1067/4739= 0.2252
(Round to the nearest thousandth as needed.)
Always P(A)= 2727/4739= 0.5754
(Round to the nearest thousandth as needed.)
(b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else?
A.
No, because there were 102 people in the survey who said they never wear their seat belt. Incorrect, an event is considered unusual if its probability (relative frequency) is low, you cannot know if it is usual or unusual just by looking at the absolute frequency of it.
B.
Yes, because P(never) < 0.05. Correct
C.
No, because the probability of an unusual event is 0. Incorrect, the probability of unusual events is low, impossible events are the ones with probability zero
D.
Yes, because 0.01 < P(never) < 0.10. Incorrect, by the definition an event is considered unusual when its probability is equal or less than 5%.
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