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Assume a binomial probability distribution with n = 40 and
p = .55. Compute the following:
a. The mean and standard deviation of the random variable.
b. The probability that x is 25 or greater.
c. The probability that x is 15 or less.
d. The probability that x is between 15 and 25 inclusive.
a) The mean is given by np, or, in this case (40)(.55) = 22.
The standard deviation = sqrt(np(1-p)) = sqrt((40)(.55)(.45))=3.146 approx.
b) The Z score at 24 is(24 - 22)/3.146 = 0.64 approx
Therefore, according to the standard normal table, the probability that x is 25 or greater is 1 - 0.7389 =
0.2611
c) The Z score at 15 is (15-22)/3.146 = -2.22 approx
Therefore, according to the standard normal table, the probability that x is 15 or less is 1 - 0.9868 =
0.0132.
d)This would be equal to the probability that it is 25 or less minus the probability that it is 14 or less.
25 or less (Z score = 0.95) ==> 0.8289
14 or less (Z score =-2.54) ==>1-0.9945=0.0055.
Therefore, the difference is 0.8289-0.0055=0.8234