Solution to Problem 1
The distributions below are binomial with number of trials n and
probability of success p. Determine which of the distributions can be
approximated by the normal distribution. If it can be approximated by
the normal distribution, give the mean and standard deviation of the normal
approximation.
 n = 75, p = 0.8
Since np =
(75)(0.8) = 60 and
nq = (75)(10.8) = 15 are both greater than
5, the binomial
distribution can be approximated by the normal distribution.
 n = 30, p = 0.9
Since np = (30)(0.9) = 27and
nq = (30)(10.9) = 3 are not both greater than
5, the binomial distribution cannot
be approximated by the normal distribution.
 n = 50, p = 0.06
Since np = (50)(0.6) = 3 and
nq = (60)(10.06) = 47 are not both greater than
5, the binomial distribution cannot be
approximated by the normal distribution.
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