SOLUTION: A binomial distribution is based on n = 15 trials and success probability p = 0 4. . What is the probability that the binomial random variable equals its mean value?

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Question 1018880: A binomial distribution is based on n = 15 trials and success probability p = 0 4. . What is the
probability that the binomial random variable equals its mean value?
Answer by mathmate(429) About Me  (Show Source):
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Question:
A binomial distribution is based on n = 15 trials and success probability p = 0 4. . What is the
probability that the binomial random variable equals its mean value?

Solution:
For the given binomial distribution with n=15, p=0.4, mean=μ=np=6.
P(k=6;15;0.4)=C%2815%2C6%29%2A0.4%5E6%2A%281-0.4%29%5E%2815-6%29
=5005%2A0.004096%2A0.010078
=0.2066

Observation:
P(k=7)=0.1771 < P(k=6)
P(k=5)=0.1859 < P(k=6)