According to CTIA, 41% of all U.S. households are wireless-only households

(no landline). In a random sample of 20 households, what is the probability that

(a) exactly 5 are wireless-only?

(b) fewer than 3 are wireless-only?

(c) at least 3 are wireless-only?

(d) the number of households that are wireless-only is between 5 and 7, inclusive?

Approach This is a binomial experiment with n = 20 independent trials. We define a success as selecting a household that is wireless-only. The probability of success, p, is 0.41. The possible values of the random variable X are x = 0, 1, 2, . . . , 20. We use Formula (1) to compute the probabilities.

Formula 1

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P(x)=Cxp(1 - p)"-x x = 0, 1, 2,...,n (1)