Multiple Choice Questions Normal approximations to discrete

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Multiple Choice Questions Normal approximations to discrete Powered By Docstoc
					         Multiple Choice Questions
Normal approximations to discrete distributions



 1. The National Broomball League claims to have a balanced league; that is,
    for any given game each team has an equal chance of winning or losing with
    no ties. Assuming the claim is true, what is the approximate probability
    that a given team will lose more than 61 games out of the 100 played?
     (a) 0.0500
    (b) 0.4918
     (c) 0.0107
    (d) 0.0082
     (e) 0.0164
    Solution: c (Uses the continuity correction so use 61.5 in the normal
    approximation)
    d would also be acceptable but it does NOT use the continuity correction


 2. The probability of getting a parking ticket when not paying for a 2-hour
    period is 0.3. What is the probability of getting at least 60 tickets if you
    park on 250 occasions for a 2-hour period and don’t pay?
     (a) 0.016
    (b) 0.019
     (c) 0.98
    (d) 0.93
     (e) 0.072
    Solution: c


 3. A professional basketball player sinks 80% of his foul shots, in the long
    run. If he gets 100 tries during a season, then the probability that he sinks
    between 75 and 90 shots (inclusive) is approximately equal to:
     (a) P r(−1.25 ≤ Z ≤ 2.5)


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        (b) P r(−1.125 ≤ Z ≤ 2.625)
        (c) P r(−1.125 ≤ Z ≤ 2.375)
        (d) P r(−1.375 ≤ Z ≤ 2.375)
        (e) P r(−1.375 ≤ Z ≤ 2.625)
       Solution: e


   4. Suppose in the University of Manitoba, 30% of the students live in apart-
      ments. If 200 students are randomly selected, then the probability that the
      number of them living in apartments will be between 50 and 75 inclusive,
      is:
        (a) .9167
        (b) .9298
        (c) .9390
        (d) .9268
        (e) .9208
       Solution: c


   5. If X has a binomial distribution with n = 400 and p = .4, the approximate
      probability of the event {155 < X < 175} is:
        (a) 0.6552
        (b) 0.6429
        (c) 0.6078
        (d) 0.6201
        (e) 0.6320
       Solution: c


   6. If in the previous question we change the interval to {155 ≤ X ≤ 175},
      the approximate probability is;
        (a) 0.4
        (b) larger than that in the previous question
        (c) smaller than that in the previous question
        (d) equal to that in the previous question
        (e) may be smaller or larger than that in the previous question
       Solution: b



c 2009 Carl James Schwarz               2
   7. Companies are interested in the demographics of those who listen to the
      radio programs they sponsor. A radio station has determined that only
      20% of listeners phoning in to a morning talk program are male. During
      a particular week, 200 calls are received by this program. What is the
      approximate probability that at least 50 of the callers are male?
        (a)   .0466
        (b)   .0212
        (c)   .1168
        (d)   .1402
        (e)   Not within ś .01 of any of the above.
       Solution: a


   8. The unemployment rate in a certain city is 8.5%. A random sample of 100
      people from the labour force is drawn. Find the approximate probability
      that the sample contains at least ten unemployed people.
        (a)   .3879
        (b)   .3245
        (c)   .3419
        (d)   .2946
        (e)   .3594
       Solution: e


   9. A politician has targeted 100 homes to visit during a week. From past
      experience, 50 percent of the households answer the bell and invite him
      in. Of this, 80 percent will agree with his policies. The approximate
      probability that the politician will get support from at least 45 households
      during a week is:
        (a)   0.1991
        (b)   0.3212
        (c)   0.8643
        (d)   0.1376
        (e)   0.1788
       Solution: d


 10. People who have been in contact with a carrier of a disease, have a 40%
     chance of contracting the disease. Suppose that the carrier of the dis-
     eases may have infected a school with 500 people. Find the approximate
     probability that at least 215 people will contract the disease.

c 2009 Carl James Schwarz                 3
        (a) .09
        (b) .91
        (c) between .05 and .34
        (d) 1.37
        (e) between 2.5% and 17%
       Solution: a
       Past performance 1993 Apr - 40% (b-22%, c-22%)




c 2009 Carl James Schwarz            4