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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.
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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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