Question

Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times that the coin shows heads. You have previously shown that all conditions have been met and that this scenario describes a binomial setting.

Determine the value of n and p and calculate the mean and standard deviation of X. Round the standard deviation to three decimal places.


n =

p =

μx =

σx =

Answer 1

In a binomial setting with X being the number of times that a fair coin shows heads in 3 flips, we have:

n = 3 (number of independent trials)
p = 0.5 (probability of success in a single trial, since the coin is fair)

The mean of X is given by:

μx = n * p

μx = 3 * 0.5

μx = 1.5

The standard deviation of X is given by:

σx = sqrt(n * p * (1 - p))

σx = sqrt(3 * 0.5 * (1 - 0.5))

σx = sqrt(0.75)

σx = 0.866 (rounded to three decimal places)

Therefore, the values are:
n = 3
p = 0.5
μx = 1.5
σx = 0.866