15 Let random variable x represent the number of heads when

15. Let random variable x represent the number of heads when a fair coin is tossed three times. Show all work. Just the answer, without supporting work, will receive no credit. (a) Construct a table describing the probability distribution. (5 pts) (b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)

Solution

a)

Using the binomial distribution formula,

P(x) = nCx p^x (1-p)^x

when n = 3, p = 0.5, we have the table:

b)

mean = n p = 3*0.5 = 1.5 [answer]

and

standard deviation = sqrt(n p (1-p)) = sqrt(3(0.5*(1-0.5)) = 0.866025 [answer]