Name Date 4. One in four adults say he or she has no trouble sleeping at night.

Question

Name Date 4. One in four adults say he or she has no trouble sleeping at night. You randomly select five adults and ask each if he or she has no trouble sleeping at night. aConstruet a binomial distribution, b) graph the distribution using a histogram, e) describe the shape of the histogram, d) find the mean, variance, and standard deviation, e) and interpret the results in the context of the real-life situation. (3 pts. ea.) Find the probability that... f)exactly-2-out of4adultssay he or she has no trouble sleeping at night ……-… g) less than 2 out of 4 adults say he or she has no trouble sleeping at night. h) more than 2 out of 4 adults say he or she has no trouble sleeping at night. 5, 2511

Explanation / Answer

n = 4

P = 1/4 = 0.25

Mean = n * P = 4 * 0.25 = 1

Variance = n * P * (1 - P)

= 4 * 0.25 * 0.75 = 0.75

Standard deviation = sqrt (0.75) = 0.866

f) P(X = x) = nCx * Px * (1 - P )n - x

P(X = 2) = 4C2 * (0.25)^2 * (0.75)^2 = 0.2109

G) P(X < 2) = P(X = 0) + P(X = 1)

= 4C0 * (0.25)^0 * (0.75)^4 + 4C1 * (0.25)^1 * (0.75)^3 = 0.7383

H) P(X > 2) = P(X = 3) + P(X = 4)

= 4C3 * (0.25)^3 * (0.75)^1 + 4C4 * (0.25)^4 * (0.75)^0 = 0.0508

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