An "instant lottery" is played by buying a ticket and scratching off a coating to reveal whether or not you have won a prize, and if so, how much. Suppose an instant lottery pays $5 with probability 0.05 and $100 with probability 0.006. Otherwise it pays nothing. Define
X = amount won for a single ticket. (You can ignore the cost of the ticket.)
-Let $S be the standard deviation of X. Which of the following is a correct interpretation of this value?
A) We would expect a randomly chosen ticket to result in a win of $D.
B) The most likely value for the amount won for a single ticket is $D.
C) The amount won for a single ticket will deviate, on average, from the expected amount won by about $D.
D) If you were to play the instant lottery many times, the average amount won per ticket would be around $D.

Question

An "instant lottery" is played by buying a ticket and scratching off a coating to reveal whether or not you have won a prize, and if so, how much. Suppose an instant lottery pays $5 with probability 0.05 and $100 with probability 0.006. Otherwise it pays nothing. Define 
X = amount won for a single ticket. (You can ignore the cost of the ticket.)
-Let $S be the standard deviation of X. Which of the following is a correct interpretation of this value?
A) We would expect a randomly chosen ticket to result in a win of $D.
B) The most likely value for the amount won for a single ticket is $D.
C) The amount won for a single ticket will deviate, on average, from the expected amount won by about $D.
D) If you were to play the instant lottery many times, the average amount won per ticket would be around $D.

Quizplus · Accepted Answer

The standard deviation measures the spread of the distribution. It tells us how much the amount won for a single ticket will deviate, on average, from the expected amount won.

An "Instant Lottery" Is Played by Buying a Ticket and Scratching