The Better Business Bureau settles 85% of complaints it receives involving new c

Question

The Better Business Bureau settles 85% of complaints it receives involving new car dealers. Suppose a sample of 90 complaints involving new car dealers is selected. Find the probability that Better Business Bureau settles less than 86 of these complaints. The Better Business Bureau settles 85% of complaints it receives involving new car dealers. Suppose a sample of 90 complaints involving new car dealers is selected. Find the probability that Better Business Bureau settles less than 86 of these complaints. The Better Business Bureau settles 85% of complaints it receives involving new car dealers. Suppose a sample of 90 complaints involving new car dealers is selected. Find the probability that Better Business Bureau settles less than 86 of these complaints.

Explanation / Answer

Solution:-

The probability that Better Business Bureau settles less than 86 of these complaints is 0.9985.

p = 0.85, n = 90

x = 86

By applying binomial distribution:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 86) = 1 - [P(x = 86) + P(x = 87) + P(x = 88) + P(x = 89) + P(x = 90)]

P(x < 86) = 1 - [0.001101 + 0.000287 + 0.0000554 + 0.0000070 + 0.000001]

P(x < 86) = 1 - 0.0015

P(x < 86) = 0.9985

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