UMUC STAT 200 quiz 2

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UMUC STAT 200 quiz 2

Question

University of Maryland University College

Stat 200 Quiz 2 – 80 points

This 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 or website 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 candy and keep it also. What is the probability of selecting 2 green candies? Leave the answers in fractional form.

2. (9 pts) A person wins in a gambling game if he gets 2 heads in 5 flips of a biased coin. The probability of getting a head is 0.7. a) Find the probability that he wins. Should he play? b) If the rules change and he wins if he gets at least 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 insurance policy to a 20-year-old female for $200. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. What is the expected cost of the insurance policy to the 20-year-old female buyer?

4. (6 pts) There is a probability of 0.05 that a lamp purchased at a given store doesn’t work. A person purchases 3 lamps. a) Define a random variable as the number of non-working lamps. What is the sample space? b) Find the probability 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 normal approximation to the binomial to approximate the probability that exactly 130 flights are on time. Compare it with the probability calculated using the binomial distribution.

6. (8 pts) The tread life of a particular brand of tire is a random variable described by a normal distribution with a mean of 65,000 miles and a standard deviation of 2500 miles. What is the probability a particular tire of this brand will last longer than 57,400 miles? What percentage of tires will last between 50,000 miles and 70,000 miles?

7. (4 pts) The time spent in the drive-thru at Wendy’s is normally distributed with a mean of 138.5 seconds and a standard deviation of 29 seconds.Wendy’s wants to initiate a policy that it will not charge any patron who has to 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 the patrons. What time would you recommend Wendy’s advertise as the maximum wait time before a free meal is awarded? Wendy’s has no way to measure 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 the dispensing machine has been identified as possessing a normal distribution with a mean of 13.5 ounces and a standard deviation of 0.1 ounce. Suppose 100 bags of chips were randomly selected from this dispensing machine.Find the probability that the sample mean weight of  these 100 bags exceeded 13.55 ounces.

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