Question

use the fact that the mean of a geometric distribution is $\mu=\frac{1}{p}$ and the variance is $\sigma^{2}=\frac{q}{p^{2}}$.
a daily number lottery chooses two balls numbered 0 to 9. the probability of winning the lottery is $\frac{1}{100}$. let x be the number of times you play the lottery before winning the first time.
(a) find the mean, variance, and standard deviation. (b) how many times would you expect to have to play the lottery before winning? it costs $1 to play and winners are paid $400. would you expect to make or lose money playing this lottery? explain.
the standard deviation is 99.5.
(round to one decimal place as needed.)
(b) you can expect to play the game $\square$ times before winning.

Explanation:

Step1: Recall the formula for the mean of a geometric distribution

The mean of a geometric distribution is \(\mu=\frac{1}{p}\). Given \(p = \frac{1}{100}\), then \(\mu=\frac{1}{\frac{1}{100}}=100\).

Step2: Answer the question about expected number of plays

The mean of the geometric distribution represents the expected number of trials until the first success.

Answer:

\(100\)