EQT173 BUSINESS STATISTICS Semester II 2014/2015

EQT173 BUSINESS STATISTICS
Semester II 2014/2015
Tutorial 3
1) State the four basic properties of binomial distribution.
2) The U.S. Department of Transportation reported that in 2009, Southwest led all domestic
airlines in on-time arrivals for domestic flights, with a rate of 0.825. Using the binomial
distribution, what is the probability that in the next six flights
a) four flights will be on time?
b) all six flights will be on time?
c) at least four flights will be on time?
d) What are the mean and standard deviation of the number of on-time arrivals?
e) What assumptions do you need to make in (a) through (c)?
3) The increase or decrease in the price of a stock between the beginning and the end of a
trading day is assumed to be an equally likely random event. What is the probability that
a stock will show an increase in its closing price on five consecutive days?
4) Assume that the number of network errors experienced in a day on a local area network
(LAN) is distributed as a Poisson random variable. The mean number of network errors
experienced in a day is 2.4. What is the probability that in any given day
a) zero network errors will occur?
b) exactly one network error will occur?
c) two or more network errors will occur?
d) fewer than three network errors will occur?
5) Based on past experience, it is assumed that the number of flaws per foot in rolls of grade
2 paper follows a Poisson distribution with a mean of 1 flaw per 5 feet of paper (0.2 flaw
per foot). What is the probability that in a
a) 1-foot roll, there will be at least 2 flaws?
b) 12-foot roll, there will be at least 1 flaw?
c) 50-foot roll, there will be more than or equal to 5 flaws and fewer than or equal to
15 flaws?
6) The U.S. Department of Transportation maintains statistics for mishandled bags per 1,000
airline passengers. In the first nine months of 2009, airlines had mishandled 3.89 bags per
1,000 passengers. What is the probability that in the next 1,000 passengers, airlines will
have a. no mishandled bags?, b. at least one mishandled bag? And, c. at least two
mishandled bags?
7) It has been reported that the overall graduation rate for football players at Division I-A
colleges and universities is 65%. SOURCE: “How Football Rates,” USA Today,
December 20, 2005, p. 12C.
a) If five players are randomly selected from the entire population of Division I-A
football players, what is the probability that at least 3 of the 5 will graduate?
b) In part (a), what is the probability that all 5 of the players will graduate?
8) An association of coffee producers has estimated that 50% of adult workers drink coffee
at least occasionally while on the job. Given this estimate:
a) For a randomly selected group of 4 adult workers, what is the probability that no
more than 3 of them drink coffee at least occasionally while on the job?
b) In part (a), what is the probability that at least 2 of these individuals drink coffee at
least occasionally while on the job?
9) During the 12 P.M.–1 P.M. noon hour, arrivals at a curbside banking machine have been
found to be Poisson distributed with a mean of 1.3 persons per minute. If X=number of
arrivals during a given minute, determine the following:
a) P(x=1)
b) P(X≤2)
c) P(2≤X≤5)
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