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Unformatted text preview: STAT/MA 416
November 14, 2011
Problem Set 33
Name:
1. There are 2000 ﬂights that arrive at the Denver airport each day, 70% of which are on
time. What is the approximate probability that strictly more than 1420 of the ﬂights are on
time in one day? Assume that the ﬂights’ delays are relatively independent. 1 2. There is a big exam tonight, and all of the 400 students are invited to attend the help
session. From past experience, the instructor ﬁnds that each student is 60% likely to attend
the help session. If the students behave independently, ﬁnd the probability that between 230
and 250 (inclusive) students attend the help session. 2 3. Bob is a professional crayon inspector. Each crayon he checks has a 5% chance of being
broken. If he checks 12,000 crayons during a certain production run, what is the approximate
probability that there are between 580 and 620 (inclusive) crayons that are broken? 3 4. If 6% of passengers are screened with an extra round of security at the airport, and
Southwest has 8 ﬂights with 180 passengers each, what is the approximate probability that
80 or more of them will receive this extra level of screening? 4 5. Jeﬀ typically makes 80% of his ﬁeld goals. Steve typically makes 60% of his ﬁeld goals.
If Jeﬀ tries 120 times to get a ﬁeld goal during a season, and Steve tries 164 times to get a
ﬁeld goal during a season, and their attempts are independent, approximate the probability
that Jeﬀ gets strictly more ﬁeld goals than Steve. 5 6. Design your own problem and solution. Create your own problem about normal
approximation to a Binomial random variable with a large parameter n. Design your problem
in such a way that you would ﬁnd it enjoyable and also interesting (i.e., not completely trivial)
if you found this problem in a probability book. Please provide the answer for your problem
too. 6 ...
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 Fall '08
 Staff
 Probability

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