In the Powerball lottery there are 59 white balls numbered 1

In the Powerball lottery, there are 59 white balls, numbered 1 to 59. Each week, five of the white balls are drawn, without replacement. In the past, the most frequently occurring white ball has been 23.

(a) In the next lottery, will the probability of drawing the number 23 be greater than 5/59, less than 5/59, or equal to 5/59?

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Before one season, the Oakland As were considered to be an average major league baseball team, predicted to win half (81) of their 162 games. They win the first six games of the season.

(b) True or false: After the first six games, the best prediction of the total number of games the Oakland As win that season is 162 out of 162.

(c) True or false: After the first six games, the best prediction of the total number of games the Oakland As win that season is still 81 out of 162.

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I survey a simple random sample of 1000 U.S. households and find out their income.

(d) True or false: By the Central Limit Theorem, the incomes in the population will have an approximately normal distribution. (e) True or false: By the Central Limit Theorem, the incomes in the sample will have an approximately normal distribution.

Solution

a. The probability of drawing the number 23 greater than 5/59. Since there are 54 white balls remaining and hence the probability will be greater than 5/59.

b. False. Sampe size of 6 matches is too small to make the predictions.

c. True. Since it was the prediction of previous season and n = 5 is too small.

d. True. The normal approximation is for population.

e. False. The normal approximation is for population, and not for sample.