A magazine reports that 5% of the population is afraid of being alone in their h

Question

A magazine reports that 5% of the population is afraid of being alone in their home during the night. If a random sample of 20 people is selected from the national population, find the folloing probabilities, (using the appropriate table in apendix),
a. tha probability that exactly five people in the sample are afraidof being alone at home
b. tha probability that at least 2 people in the sample are afraid of being alone at home
c. the probability that all 20 people in the sample are NOT afraid of being alone.

Explanation / Answer

a. tha probability that exactly five people in the sample are afraidof being alone at home

P(5) = 20C5 (0.05)5(0.95)15 = 0.0518

b. tha probability that at least 2 people in the sample are afraid of being alone at home

The probability that “at least 2 people” are afraid is equal to:

1 – P(at most 1 person is afraid) = 1 – P(0) – P(1)

P(0) = 20C0 (0.05)0(0.95)20 = 0.3585
P(1) = 20C1 (0.05)1(0.95)19 = 0.3774
P(2 or more) = 1 – 0.3585 – 0.3774 = 0.2641

c. the probability that all 20 people in the sample are NOT afraid of being alone.

P(20) = (0.95)20 = 0.3585

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