If the lottery is fair what shape of histogram will she get?

Answer 1

In a state lottery, a player can buy a ticket that displays exactly 6 two-digit numbers having values in the range from 01 to 60. In a twice-a-week drawing, 6 numbered ping-pong balls are drawn at random from a hopper, and a ticket whose numbers match all 6 balls wins the jackpot.

A high-school statistics student wishes to test whether the lottery drawings are fair. For every drawing during a year, she records the six winning numbers. At the end of the year (after 104 drawings) she plots all the winning numbers with a histogram using the classes 01-10, 11-20, 21-30, 31-40, 41-50, and 51-60.

If the lottery is fair, what shape of histogram will she get?

Uniform

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Theoretically, each bar of the histogram should have the same length, if the ball-drawing process is truly random. In this case, 104 x 6 = 624 numbers are drawn over the course of the year. Since the numbers are classed into 6 groups (of 10 each), each group should have about 104 numbers in it.

In fact, from simulations of this lottery, the heights of the bars representing a year of drawings will typically range from about 93 to about 119. The "Law of Large Numbers" says that the more times this experiment is repeated, the closer the average height of each bar will approach the theoretical value of 104

.