SOLUTION: Suppose a recent survey by Fade Napoli found that 84% of their customers were satisfied with their most recent meal. a.Calculate the probability that exactly four of the next five

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Question 848324: Suppose a recent survey by Fade Napoli found that 84% of their customers were satisfied with their most recent meal.
a.Calculate the probability that exactly four of the next five customers will be satisfied.
b.Calculate the probability that less than four of the next five customers will be satisfied.
c.Calculate the mean and standard deviation of this distribution.

Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website!
X~ Binomial(n=5, p=.84)
a)
P[X=4] = (5 choose 4)*(.84)^4*(.16)^1 = .3983
b) Use complement since we're talking about 1 calculation as opposed to 4. I say 1 because we already calculated P[X=4].
So we calculate P[X=5] = (5 choose 5) *(.84)^5 *(.16)^0 = .4182
then P[X<4] = 1-P[X>=4] = 1-(P[X=4] + P[X=5]) = 1-(.3983+.4182) = .1835
c) mean of binomial : np = 5*.84 = 4.2
sd of binomial : sqrt(npq) = sqrt(4.2*.16) = .82