Math 227 Test 2 Ch5. Name

Transcription

1 Math 227 Test 2 Ch5 Name Find the mean of the given probability distribution. 1) In a certain town, 30% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. x P(x) ) Provide an appropriate response. Round to the nearest hundredth. 2) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are , , , , and , respectively. Find the standard deviation for the probability distribution. 2) Answer the question. 3) Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games? 3) Provide an appropriate response. 4) A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is , what is the expected value for the insurance policy? 4) 1

2 Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 5) Choosing 4 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time 5) without replacement, keeping track of the number of red marbles chosen. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 6) n = 7, x = 4, p = 0.5 6) Find the indicated probability. Round to three decimal places. 7) A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. 7) Find the indicated probability. 8) A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others. 8) 2

3 Find the standard deviation,, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 9) n = 38; p = 0.4 9) Use the given values of n and p to find the minimum usual value µ - 2 and the maximum usual value µ + 2. Round your answer to the nearest hundredth unless otherwise noted. 10) n = 237, p = ) Solve the problem. 11) A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch. 11) Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2 or greater than µ ) According to AccuData Media Research, 36% of televisions within the Chicago city limits 12) are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 919 of the 2500 televisions are tuned to "Eyewitness News"? 3

4 Use the Poisson Distribution to find the indicated probability. 13) The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.8. Find the probability that in a randomly selected year, the number of lightning strikes is 0. 13) Find the indicated mean. 14) The mean number of homicides per year in one city is Suppose a Poisson distribution will be used to find the probability that on a given day there will be fewer than 4 homicides. Find the mean of the appropriate Poisson distribution (the mean number of homicides per day). Round your answer to four decimal places. 14) Use the Poisson model to approximate the probability. Round your answer to four decimal places. 15) The rate of defects among CD players of a certain brand is 1.5%. Use the Poisson approximation to the binomial distribution to find the probability that among 430 such CD players received by a store, there are exactly three defective CD players. 15) 4

5 Answer Key Testname: MATH 227 TEST 2 WINTER ) µ = ) = ) No 4) -$ ) Not binomial: the trials are not independent. 6) ) ) ) = ) Minimum: 45.92; maximum: ) ) No 13) ) )