Question

A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands. (Round your answers to three decimal places.)

(a)

What is the probability that eleven or more homeowners would state a preference for brand A?

(b)

What is the probability that eleven or more homeowners would state a preference for either brand A or brand B?

You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

Here, n = 15 , p =0.5

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)

P(x> =11) = 1- (x < =10)
= 0.059

b)

P(11 or more prefer A or B) = 2*P(X>=11) [as p = 1-p = 0.5]
= 2 * 0.059
= 0.118