Question

One in four adults say he/she has no trouble sleeping at night. You randomly select five adults and ask if he/she has no trouble sleeping at night. Find the probability that none of the adults have no trouble sleeping Find the probability at least 1 adult has no trouble sleeping Find the mean and standard deviation.

Answer 1

Probability of adults that has no trouble sleeping at night = 1/4 = 0.25

Sample size, n = 5

Using binomial function,

Probability that none of the adults have no trouble sleeping, P(X = 0) =

Probability that at least one adult has no trouble sleeping, P(X >= 1) = 1-P(X<1)

= 1- P(X=0)

= 1- 0.2373 = 0.7627

Mean, µ = n*p = 1.25

Standard deviation, σ = √(n*p*(1-p)) = 0.9682