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In the DISTR menu, we have two binomial functions, binompdf and binomcdf.. The i

ID: 3208933 • Letter: I

Question

In the DISTR menu, we have two binomial functions, binompdf and binomcdf.. The inputs for each is the same:
     n = number of trials, p = probability of success, X = # of successes.

But binompdf is the binomial probability distribution function, and binomcdf is the binomial cumulative distribution function. That is,

P(X = k) = binompdf (n, p, k) is the probability of exactly k successes
                       in n trials.


P(X < k) = binomcdf (n, p, k) is the probability of at most k successes
                       in n trials.


Suppose we have a binomial distribution with n = 20 and p = 0.43, and find the following probabilities.    

a) P(X = 12)

b) P(X > 7)


c) P(X < 15)

Explanation / Answer

a) P(X= 12)

= binompdf (20, 0.43, 12)

= 0.0561

b) P(X > 7)

= 1 - P(X <= 7)

= 1 - binomcdf (20, 0.43, 7)

= 1 - 0.3132

= 0.6868

c) P(X < 15)

= P(X <= 15) - P(X = 15)

= binomcdf (20, 0.43, 15) - binompdf (20, 0.43, 15)

= 0.9992 - 0.003

= 0.9962