It is reported that 27% of American households use a cell phone exclusively for

Question

It is reported that 27% of American households use a cell phone exclusively for their telephone service. In a sample of sixteen households, find the probability that:

No household uses a cell phone as their exclusive telephone service. (Round your answer to 4 decimal places.)

Exactly 9 households exclusively use a cell phone for telephone service. (Round your answer to 4 decimal places.)

Find the mean number of households exclusively using cell phones. (Round your answer to 4 decimal places.)

It is reported that 27% of American households use a cell phone exclusively for their telephone service. In a sample of sixteen households, find the probability that:

Explanation / Answer

p = 0.27, q = 1 - p = 1 - 0.27 = 0.73

For Binomial Probability = nCr * (p)r * (q)n-r, where n = number of trials and r is the number of successes.

Where nCr = n! / [(n-r)!*r!]

Here n = 16

(a) No Household uses a cell phone : r = 0 and n - r = 16 - 0 = 16

P(0) = 16C0 * (0.27)0 * (0.73)16 = 0.0065

(b) Exactly 9 Households use a phone : r = 9 and n - r = 16 - 9 = 7

P(0) = 16C9 * (0.27)9 * (0.73)7 = 0.0096

(c) Mean = n * p = 16 * 0.27 = 4.32

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