# 1. Answer the following questions and justify your answer with an explanation.

a) In the Powerball lottery, there are 59 white balls, numbered 1 to 59. Each week, ﬁve of the white balls are drawn, without replacement.

I. Show that the probability of drawing any specific number between 1 and 59, for example 23, is .

II. In the past, the most frequently occurring white ball has been 23. In the next lottery, will the probability of drawing the number 23 be greater than , less than , or equal to ? Explain.

b) I survey a simple random sample of 1000 U.S. households and ﬁnd out their income. True or False: By the Central Limit Theorem, the incomes in the population will have an approximately normal distribution.

c) I survey a simple random sample of 1000 U.S. households and ﬁnd out their income. True or False: By the Central Limit Theorem, the incomes in the sample will have an approximately normal distribution.

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