a)If the sampling is done with replacement, what is the probability that two of the switches are heavy duty? Identify the distribution and parameter(s) used. (5 points)

b)If the sampling is done without replacement. What is the probability that three of them are heavy duty? Identify the distribution and parameter(s) used. (5 points)

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c)Another box of switches arrives at the company and all of the switches were mixed together. There are now a total of 500 switches, of which 120 are heavy duty. The shipping clerk will take a sample of 10 switches at random without replacement. Write out the expression (do not solve)to determine the probability that you have exactly 4 heavy duty switches. Identify the distribution and parameter(s) used. (4 points)

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d)Is there an approximation that can be used for part c)? Explain why or why not. If there is an appropriate approximation name that distribution and its parameter(s). Additionally, find the probability that you have exactly 4 heavy duty switches. (5 points)

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5 8.At a child’s birthday party, there is a piñata game. The piñata isfilled with candy and the point of the game is to break open the piñata with a bat swung by a blindfolded participant so that the candy spills out for all to grab. Assume that each swing of the bat is independent and the bat hits the piñata hard enough to break it open on average one out of every 10 swings. Each child gets only one swing of the bat. a)Let S be the number of swings until the piñata is hit hard enough to break. What distribution and parameter(s) are appropriate? (3 points)

b)What is the probability that the piñata breaks open on the 12thswing? (3 points)

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