QUESTIONS 1-4 refer to the following 20 test scores:

1. Find the sample median.
2. Find the first quartile.
3. Find the sample mean.
4. Find the sample standard deviation.
   QUESTIONS 5-8 refer to length in the population of rainbow trout in a certain Rocky Mountain watershed area which is known to be normally distributed with mean 11 inches and standard deviation 5 inches.
5. If a rainbow trout from the specified area is chosen at random, what is the probability that it has length between 7 inches and 13 inches?
6. If a rainbow trout from the specified area is chosen at random, what is the probability that it has length between 7 inches and 13 inches GIVEN that the length is between 5 and 15 inches?
7. If 5 randomly chosen rainbow trout from the specified area are laid out head to tail, what is the probability their total length will be between 50 and 60 inches?
8. If x is the length for which 80 percent of the population of rainbow trout has length less than x and 20 percent of the population of rainbow trout has length more than x, then x=

?

QUESTIONS 9-11 refer to events A and B with P(A) = .5, P(B) = .4, and P(A given B) = .7.

9. P(A and B) =

10. P(A but not B) =

11 . P(A or B)

QUESTIONS 12-17 refer to a box containing envelopes. There are 90 envelopes in the box, of which 3 each contain a single one hundred dollar bill, 8 each contain a single fifty dollar bill, 14 each contain a single twenty dollar bill, 18 each contain a single ten dollar bill, and the remaining 47 envelopes each contain a single one dollar bill. We randomly draw 20 envelopes from the box WITH replacement, one after another.

12. The probability that the third envelope drawn contains a twenty dollar bill is=

13. The probability that exactly six of the drawn envelopes each contain AT LEAST twenty dollars is =?

14. The expected number of drawn envelopes that each contain AT LEAST twenty dollars is=

15. The standard deviation in the number of envelopes drawn that each contain AT LEAST twenty dollars is =

16 The expected monetary value of the contents of the first envelop drawn is =?

17 The expected monetary value of the total of all the bills from the 20 drawn envelopes is=

QUESTIONS 18-20 refer to the following distribution for a random variable X

1. :Find the population mean.
2. Find the population standard deviation.
3. Find the probability that X is less than 140.
   QUESTIONS 21-22 refer to a deck of cards containing a joker in addition to the usual 52 cards of which 13 are clubs. The deck is shuffled so the cards are in random order and set down on a table.
4. The probability that the middle card in the deck is the joker is

22. The probability that the middle card is one of the thirteen clubs is ?

QUESTIONS 23-25 refer to a statistician studying burn life in light bulbs for the Consumer Protection Agency. In a sample of 12 light bulbs produced at Acme Corporation he finds that the average burn life is 736 hours with a sample standard deviation of 37 hours. He assumes that burn life in the population of light bulbs under study is actually normally distributed.

1. Given he does not know the population standard deviation, then what is the MARGIN OF ERROR for the 90 percent confidence interval for true mean light bulb burn life based on his data?
2. Given he does not know the population standard deviation, then what is the p-value or significance of his data as evidence in favor of the conclusion that the true mean light bulb burn life exceeds 700 hours?
3. What is the distribution used to compute this p-value?
4. If we are trying to establish, at level of significance .05, that the true mean weight of laboratory guinea pigs is more than two pounds and the p-value of our data supporting this hypothesis is .31, then

1. there is a 31 percent probability that the null hypothesis is true
2. we definitely reject the null hypothesis
3. our data is very contradictory of the null hypothesis
4. there is a 31 percent chance that the null hypothesis is false
5. none of the above

27. Suppose Batman and Robin are in the Bat Cave each testing one of two new brands of cable for use in their climbing on the roofs of buildings in Gotham City, working independently of each other. They are both assuming that breaking strength is normally distributed, but Batman is using a larger sample size than Robin. As luck would have it, both arrived at the same value of the sample mean which in fact was a number bigger than 2500 pounds for mean breaking strength, and they both found the same value for the sample standard deviation of their data. They both have as the alternate hypothesis that the true mean breaking strength of the cable exceeds 2500 pounds. Let b be the p-value of Batman's data and let r be the p-value of Robin's data. Then

1. b is less than .5 and r exceeds .5
2. r is less than .5 and b exceeds .5
3. both b and r are less than .5, but b is less than r
4. both b and r are less than .5, but r is less than b
5. both b and r exceed .5 and b exceeds r

28. Batman has determined that for cable to be safe for use in climbing on buildings, its mean breaking strength must exceed 2500 pounds. He and Robin are testing Acme light cable at the 0.01 percent level of significance (a = .0001) to see if it is safe for their climbing. They seek to establish that the true mean breaking strength of Acme light cable exceeds 2500 pounds. If their data establishes that Acme light cable is strong enough to be safe for building climbing (true mean breaking strength over 2500 pounds), at the 0.01 percent level of significance, then

1. there is a .01 percent probability that the cable is not safe
2. there is a .01 percent probability that the cable really is safe
3. if the rope is not safe, there is still a .01 percent probability their method could lead them to conclude it is safe
4. if the rope is safe, there is still a .01 percent probability their method could lead them to conclude it is not safe
5. none of the above

1. If blood pressure in the population of Indian elephants is normally distributed, then in a random sample of 11 Indian elephants what is the probability that more than 7 have above average blood pressure?
   QUESTIONS 30-33 refer to a traffic engineer monitoring bus traffic along Main Street in a large metropolitan area. The bus company claims that buses arrive at each stop on average every 10 minutes, 24 hours a day, seven days a week independently of the time of day or the day of the week or the location of the stop.
2. If the bus company's claim is true, then how many buses are expected to arrive at the engineer's stop during the next half hour?
3. If the bus company's claim is true, what is the probability that no more than 2 buses arrive at the engineer's stop during the next half hour?
4. If the bus company's claim is true, what is the probability that we have to wait at the bus stop more than twenty minutes for a bus?
5. If the bus companies claim is true and the random variable X is defined as the number of buses that arrive at the engineer's stop during the 3 hour period beginning at 2 P.M. on any randomly chosen day, then what is the standard deviation of X?
   QUESTIONS 34-36 refer to the random variable Y which is uniformly distributed between 120 and 150.
6. The expected value of Y is?
7. If the random variable T is defined as the total of 6 independent observations of Y, then the STANDARD DEVIATION of T is?
8. If the random variable W is defined as the average of 6 independent observations of Y, hen the EXPECTED VALUE of W is?

QUESTIONS 37-40 refer to a researcher studying preference for Donald over Mickey for mayor of Duckburg in the upcoming election. Suppose that in a random sample of 2,000 registered voters in Duckburg the researcher finds that 56 percent of those sampled prefer Donald for mayor over Mickey.

1. Based on this data, what is the 99 percent confidence interval for the true percentage of registered voters in Duckburg that prefer Donald for mayor?
2. What is the p-value of this data as evidence that the true proportion of registered voters in this population who prefer Donald is NOT EQUAL to 55 percent?
3. Of the 2,000 registered voters sampled, if we assume the true percentage of those who favor Donald over Mickey is 55 percent, then how many of those sampled do we expect to favor Donald over Mickey for mayor of Duckburg?
4. What would be the standard deviation in the number who favor Donald over Mickey in the sample of 2,000 if the true percentage favoring Donald over Mickey for mayor of Duckburg is actually 55 percent?

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