If a gambler places a bet on the number 14 in roulette, he or she has a 1/38 probability of winning.

Question

a) find the mean and standard deviation for the number of wins of gamblers who bet on the number 14 eighty times.

Is the procedure an example of a binomial distribution?

State the given   n =… ; p =…..; q = …;

The mean is:

The standard deviation is:

b) Would 0 wins in 80 bets be an unusual low number of wins? Why, show work?

Answer 1

This is a binomial experiment with the number of wins being binomially distributed.

n = 80, p = 1/38 = 0.026

the mean is 80/38 = 2.11

the standard deviation is (80* 0.026 * 0.974) = 1.42

x = number of wins

using binomial formula

P(x = 0) = 80!

---- (0.026)^0*(0.974)^80 = 0.12

0! 80!

Since probability exceeds 0.05, it would not be very unusual.