Roulette If you place a bet on the number 7 in roulette, you have a 1/38 probability of winning.

a. Find the mean and standard deviation for the number of wins for people who bet on the number 7 fifty times.

b. Would 0 wins in 50 bets be an unusually low number of wins?

Problem 18BSC

Answer:

Step1 of 2:

We have If you place a bet on the number 7 in roulette, you have a 1/38 probability of winning.

That is n = 50 and p = 1/38.

The mean and standard deviation for the number of wins for people who bet on the number 7 fifty times is given by

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 50 and p = 1/38 = 0.0263.

q = 1 - p

= 1 - 0.0263

= 0.9736.

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

With mean E(x) = np and variance var(x) = npq

Consider,

E(x) = np

= 500.0263

= 1.315

Therefore,E(x) = 1.315

var(x)...