The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : $$\begin{array} { | c | c | }
\hline X & P [ X ] \
\hline 0 & 0.95 \
\hline 10 & 0.049 \
\hline 100 & 0.001 \
\hline
\end{array}$$ Which of the following best describes the standard deviation of X ?
A)14.552 in $2
B)3.815 in $
C)0.348 in $
D)None of these choices are correct

Question

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : $$\begin{array} { | c | c | } 
\hline X & P [ X ] \
\hline 0 & 0.95 \
\hline 10 & 0.049 \
\hline 100 & 0.001 \
\hline
\end{array}$$ Which of the following best describes the standard deviation of X ?
A)14.552 in $2
B)3.815 in $
C)0.348 in $
D)None of these choices are correct

Quizplus · Accepted Answer

The standard deviation is calculated using the formula for discrete random variables. The variance is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities. The standard deviation is the square root of the variance, which is approximately 3.815 in this case.

The Lottery Commission Has Designed a New Instant Lottery Game XP[X]00.95100.0491000.001\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}X010100​P[X]0.950.0490.001​​

The Lottery Commission Has Designed a New Instant Lottery Game $\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}$