suppose a recent survey conducted by UCA\'s Christian Cafeteria found that 84% o

Question

suppose a recent survey conducted by UCA's Christian Cafeteria found that 84% of its customers were satisfied with their most recent meal. Suppose you conduct a s next 5 customers, and the results follow a binomial distribution. Round to 4 significant decimal places urvey of the (10 points) Calculate the probability that exactly four of the next five customers chosen at random will be satisfied. a. (10 points) Calculate the probability that less than four of the next five customers chose at random will be satisfied. b.

Explanation / Answer

X ~ Binomial (n,p)

Given,

n = 5 , p = 0.84

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X = 4) = 5C4 0.844 0.161

= 0.3983

b)

P( X < 4) = 1 - P( X >= 4)

= 1 - { P( X = 4) + P( X = 5) }

= 1 - { 5C4 0.844 0.161 + 5C5 0.845 0.160 }

= 1 - 0.8165

= 0.1835

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