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

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

RELATED QUESTIONS
In a recent study, it was found that 40% of customers are unsatisfied with their bank. In (answered by reviewermath)

n a recent study, it was found that 40% of customers are unsatisfied with their bank. In... (answered by ewatrrr)

A hair salon claims that 90% of their customers are satisfied. However, Toni who recently (answered by Theo)

At a local Wendy's, a survey showed that out of 9,200 customers eating lunch, 1,000... (answered by Mathtut)

Please help with this probability question. Thank You! A recent survey found that 40%... (answered by stanbon)

John Isaac Inc., a designer and installer of industrial signs, employs 60 people. The... (answered by CPhill)

Two hundred eighty-five viewers were asked if they were satisfied with TV coverage of a... (answered by Fombitz)

A Travel Weekly International Air Transport Association survey asked business travelers... (answered by VFBundy)

A Travel Weekly International Air Transport Association survey asked business... (answered by VFBundy)