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University of Maryland University CollegeStat 200Quiz 2 â 80 pointsThis is an open-book, open-notes quiz. A calculator, Excel or other software may be used and are encouraged.You may add spaces as needed to show your work. You must show your work OR cite your calculator app orwebsite app to receive full credit. An answer that consists of simply a number will receive no credit.1. (5 pts) A bag contains 5 white, 10 blue, 12 red, 7 yellow, and 6 green candies.A candy is selected from the bag and kept. You then draw a second candyand keep it also. What is the probability of selecting 2 green candies? Leavethe answers in fractional form.2. (9 pts) A person wins in a gambling game if he gets 2 heads in 5 flips of abiased coin. The probability of getting a head is 0.7. a) Find the probabilitythat he wins. Should he play? b) If the rules change and he wins if he gets atleast 4 heads in 5 flips, what is the probability that he wins?3. (4 pts) A life insurance company sells a $250,000 1-year term life insurancepolicy to a 20-year-old female for $200. According to the National VitalStatistics Report, 58(21), the probability that the female survives the year is0.999544. What is the expected cost of the insurance policy to the 20-yearold female buyer?4. (6 pts) There is a probability of 0.05 that a lamp purchased at a given storedoesnât work. A person purchases 3 lamps. a) Define a random variable asthe number of non-working lamps. What is the sample space? b) Find theprobability distribution.5. (6 pts) Flight 215 from Orlando to Los Angeles is on time 90% of the time.Randomly select 150 flights from Orlando to Los Angeles and use the normalapproximation to the binomial to approximate the probability that exactly 130flights are on time. Compare it with the probability calculated using thebinomial distribution.6. (8 pts) The tread life of a particular brand of tire is a random variabledescribed by a normal distribution with a mean of 65,000 miles and astandard deviation of 2500 miles. What is the probability a particular tire ofthis brand will last longer than 57,400 miles? What percentage of tires willlast between 50,000 miles and 70,000 miles?7. (4 pts) The time spent in the drive-thru at Wendyâs is normally distributedwith a mean of 138.5 seconds and a standard deviation of 29 seconds.Wendyâs wants to initiate a policy that it will not charge any patron who hasto wait more than a certain amount of time for an order in the drive-thru.Management does not want to give away free meals to more than 1% of thepatrons. What time would you recommend Wendyâs advertise as themaximum wait time before a free meal is awarded? Wendyâs has no way tomeasure fractions of seconds so your answer should be a whole number.8. (4 pts) The amount of corn chips dispensed into a 13-ounce bag by thedispensing machine has been identified as possessing a normal distributionwith a mean of 13.5 ounces and a standard deviation of 0.1 ounce. Suppose100 bags of chips were randomly selected from this dispensing machine. Findthe probability that the sample mean weight of these 100 bags exceeded13.55 ounces.
