Question

According to Information Resources, which publishes data on market share for various products,
Oreo controls about 10% of the market for cookies brands. Suppose 20 purchasers of cookies are
selected randomly from the population. What is the probability that fewer than four purchasers
choose Oreos?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

0.867

Step-by-step explanation:

Given:- Oreo controls 10% of market.

To Find:- Probability that less than 4 purchasers choose Oreos when 20 are selected randomly.

Solution:-

The formula of Binomial distribution is $nC_{x} p^{x} q^{n-x}$.

Oreo controls 10% of market , so

Probability of choosing Oreo = 10/100 = 0.1

Here, n = 20, p = 0.1, q = (1 - 0.1) = 0.9

Probability that less than 4 purchasers choose Oreo i.e.

P(x) = P(0) + P(1) + P(2) + P(3)

     =  $20C_{0} (0.1)^{0} (0.9)^{20-0}+ 20C_{1} (0.1)^{1} (0.9)^{20-1}+\\20C_{2} (0.1)^{2} (0.9)^{20-2}+20C_{3} (0.1)^{3} (0.9)^{20-3}$

     = $(0.9)^{20} + 20(0.1)(0.9)^{19} + 190(0.01)(0.9)^{18} + 1140(0.001)(0.9)^{17}$

    = 0.122 + 0.270 + 0.285 + 0.190

    = 0.867

Hence, when 20 cookie purchasers are randomly selected about 86.7% of the purchasers will select Oreos.

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