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1. The payouts for the Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00. Find the mean and standard deviation of the payout. Hint: Don’t forget to include the cost of the ticket and its corresponding probability.Divisions Payout Odds ProbabilityFive plus Powerball $50,000,000 146,107,962 0.000000006844Match 5 200,000 3,563,609 0.000000280614Four plus Powerball 10,000 584,432 0.000001711060Match 4 100 14,255 0.000070145903Three Plus Powerball 100 11,927 0.000083836351Match 3 7 291 0.003424657534Two Plus Powerball 7 745 0.001340482574One Plus Powerball 4 127 0.007812500000Zero plus Powerball 3 69 0.0142857142862. An auditor for Health Maintenance Services of Georgia reports 40% of policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records.a. How many of the policyholders would you expect to have filed a claim within the last year?b. What is the probability that 10 of the selected policyholders submitted a claim last year?c. What is the probability that 10 or more of the selected policyholders submitted a claim last year?d. What is the probability that more than 10 of the selected policy holders submitted a claim last year?32. A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyone’s privacy.a. How much toothpaste would you expect to be remaining in the tube?b. What is the standard deviation of the amount remaining in the tube?c. What is the likelihood there is less than 3.0 ounces remaining in the tube?d. What is the probability there is more than 1.5 ounces remaining in the tube?37. A recent report in USA Today indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a standard deviation of $90 per month.a. What percent of the families spend more than $30 but less than $490 per month on food?b. What percent of the families spend less than $430 per month on food?c. What percent spend between $430 and $600 per month on food?d. What percent spend between $500 and $600 per month on food.
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