MATH 1324Quiz 6Show all work in the space provided. Credit will be given only for work that is clear and readable.Please staple all pages together before turning in the quiz.23. Give all answers as decimals correct to 4 significant decimal digits. A company advertises that its newtoothpaste will prevent tartar buildup. It claims that 40% of people will have less tartar after three months ofusing the toothpaste. To justify the claim a clinical experiment is run with 20 people using the toothpastefor three months. Find the probability thata) only 4 of the twenty will have less tartar.a) ___________________b) at least 4 of the twenty will have less tartar.b) ___________________24. A new drug claims that it is 85% effective when used to treat patients that have a terrible infection soall such patients with the infection at a local hospital are treated with this new drug. About 5% of thepatients in a local hospital have this terrible infection. Give all answers as decimals correct to 4 significantdecimal digits.a) What is the probability that a person hospitalized for this terrible infection is cured giventreatment by this new drug?a) ___________________b) What is the probability that a person recently released from this hospital was treated and curedof this terrible infection by this new drug?b) ___________________c) If 20 people recently released from this hospital are surveyed, what is the probability that 2 ofthem were treated and cured of this terrible infection?c) ___________________25. Three cards are drawn from a standard deck. Write probabilities as reduced fractions.a) How many 3-card hands are possible?b) What is the probability that all three cards are diamonds?c) What is the probability that all three cards are in the same suit?d) What is the probability that all three cards are face cards?e) What is the probability of three of a kind?f) What is the probability of having a pair (exactly 2 of a kind)?g) What is the probability of having (exactly) 2 cards of the same suit?a) _____________b) _____________c) _____________d) _____________e) _____________f) _____________g) _____________26. You draw one card from a standard deck of playing cards. If you pick a heart, you will win $10. If youpick a face card, which is not a heart, you win $8. If you pick any other card, you lose $6. Do you want toplay?a hearta face card not a heartany other cardxpProbabilities must be exact fractions and not decimal numbers.27. At Tucson Raceway Park, your horse, Soon-to-be-Glue, has odds of 19:1 against coming in first place,odds of 9:1 against coming in second place, and odds of 3:1 against coming in third place. First place pays$4,500 to the winner, second place $3,500 and third place $1,500. Is it worthwhile to enter the race if itcosts $1,000? Be careful here — you were given odds against and not probabilities!first placesecond placethird placexpProbabilities must be exact fractions and not decimal numbers.28. A construction company has just received a building contract. From past experience, the companyestimates there is a 55% chance of making a $500,000 profit, a 8% chance of breaking even, and a 37%chance of losing $200,000, depending on weather conditions and other factors. What is the expected valueof the companyâs contract?
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