# 1)Determine the mean, median, mode, range, and standard deviation of the following numbers.

1)     Determine the mean, median, mode, range, and standard deviation of the following numbers. It may influence how you calculate this to know that they are the temperatures of 5 freezers sampled from a group of 20. Be sure to use the correct symbols where applicable.  4,7,7,18,20

2)     What are the populations of San Diego, CA, USA, China, and the world? About how many miles around is the Earth? About how many people died as a direct result of World War II? How about from the Spanish Flu?

3)     You have \$3000. You have a financial goal: In 25 years you would like this to grow to \$10,000. What average interest rate must you achieve? Hint: use this formula:                                    Average interest rate = (End Amount/Beginning Amount)^(1/time)   -1

4)     A bucket contains 18 blue slips of paper and 27 Green. If you select one at random , what is the probability that you will get a green on? If you select 2 without replacement, what is the probability that that the first one will be green and the second one will be blue? If you select 5 without replacement, what is the probability that all five will be blue?

5)     If the odds of an event happening are 1/4, what is the probability of it happening?

6)     You have a combination lock. There are four numbers to any combination. The dial contains 40 numbers. Assuming that no two consecutive numbers can be the same, how many combinations are possible?

7)     A company has devised a test for a new emergent disease. When 200 people who have it were tested, it was found that 180 tested positive. When 300 people who did not have it were tested 10 tested positive. The prevalence of this disease in the population is 2%. Determine the 5 measures of accuracy. If a person subsequently tests positive, which measure is he interested in? What if a person tested negative?

8)     If we are going to award the same prize to 8 people out of a group of 20, how many ways might this play out? What if the prizes are all different?

9)     Refer to the question with the pieces of paper in a bucket. If you select 8, one at a time with replacement, what is the probability that 6 will be Blue?

10)  A piece of equipment’s defect rate is 4%. We will need at least 9. We want to be 97% sure we achieve this. What is the fewest number we should order?

11)  A new drug has been developed and will be tested to see if it is more effective than a placebo. We administer the drug to a group of 730 randomly chosen people. 610 of them report a positive effect. Additionally we administered a placebo to 943 people. Amongst them 640 reported a positive effect. Construct a confidence interval comparing the two groups and draw the correct conclusion. Let c = 95%

12)  A bucket contains 13 blue slips of paper and 27 Green. If you select one at random , what is the probability that you will get a green one? If you select 2 without replacement, what is the probability that that the first one will be green and the second one will be blue? If you select 5 without replacement, what is the probability that all five will be blue? Also, if the odds of an event happening are 1/4, what is the probability of it happening? Finally, you have a combination lock. There are four numbers to any combination. The dial contains 40 numbers. Assuming that no two consecutive numbers can be the same, how many combinations are possible?

13)  Explain with examples type I and II errors. Do not use any of the examples your teacher used. Do not use any examples the text uses. Also explain how this affects the approval of drugs by the FDA.

14)  We are a trucking company who has purchased our tire for many years from the Long-Haul Tire tire concern. A competitor, I-Tire, offers to sell us tires for the same price. The advantage, so sayeth I-Tire, is that their tires will last longer. To test this assertion we conducted the following experiment: 49 of the old company’s tires we run until failure. The mean mileage to failure was 40000 miles with a standard deviation of 3000 miles. 23 I-Tires were also run until failure with a mean of 41000 miles and a standard deviation of 200 miles. Construct a confidence interval comparing the two groups and draw the correct conclusion.  Let c = 99%

15)  We wish to determine the Profit/item sold. Consider the following information and compute the aforementioned quantity. Also explain why this is a more appropriate number to calculate than the Profit/Warranty sold. A. Replacement Cost = \$400,  B. Mean time to replacement = 9.3 years, C. Standard Deviation = 1.8, D. Length of warranty = 6 years, E. cost of warranty =\$100, F. proportion of buyers of the item who will purchase the warranty = 80%.

16)  We wish to determine the proportion of tuna in the pacific that are contaminated with mercury. A random sample of 1300 tuna had 75 contaminated fish. At the 90% level of confidence, construct a confidence interval which gives an estimate of the true proportion of contaminated fish.  Would this affect your intake of tuna?

17)  A company has devised a test for a new emergent disease. When 200 people who have it were tested, it was found that 150 tested positive. When 300 people who did not have it were tested 5 tested positive. The prevalence of this disease in the population is 2%. Determine the 5 measures of accuracy. If a person subsequently tests positive, which measure is he interested in? What if a person tested negative?

18)  We wish to determine the actual alcohol content of a particular brand of beer. After obtaining a random sample of 30, we found the mean to be 4.8% with a standard deviation of .7%. Construct a confidence interval estimating the population mean. Use the 95% level of confidence.

19)  We wish to estimate the population of mice in a 100 acre parcel of land. To this end, we randomly captured (we might wonder how this was done!) 75 mice. They were subsequently tagged and released. Later, and random roundup of 420 mice had 50 tagged in their midst. What is you estimate of the total number of mice? You must use the “black box” method of estimation.

20)  How far around is the Earth? How far away is the Moon? How far away is the Sun? How far away is Neptune? To the nearest star not our sun? How far across the Galaxy? Across the visible universe?

21)  A drug company has developed an anti-depression drug. We tested a group of 15 people by measuring their levels of depression before and after taking the drug and found a mean difference of 5.7 with a standard deviation of 1.3. We test another group with a placebo and found a mean difference of 5.5 with a standard deviation of 0.1. At the 99% level of confidence construct a confidence interval which estimates the difference. Draw an appropriate conclusion.

22)  Hundreds of nurses have applied for 6 open positions at Doctors without Boarders. After a careful screening process, we are left with 30 highly qualified candidates. Among them are 6 over the age of 40. To ensure fairness, the 5 were chosen through a drawing of names from a hat. We announced, it was noticed that 4 were from the 40 and over category. Compute the probability of this happening. Explain why this is or is not an appropriate probability to help understand this outcome.

23)  It had been observed that some new soldiers are, frankly, just bad shots. It was therefore determined that new recruits who score in the bottom 5% will be dropped from training. We know that the average test score on the rifle range is 580 with a standard deviation of 42. Determine a score separating the bottom 5% from the higher scoring candidates. When looking for possible Special Forces candidates, we want to start with those who are in the top 1%. What score separates the top 1% from the rest?

24)  If the mean weight of new recruits is 170 lbs with a standard deviation of 12 lbs, what percent of recruits weigh less than 150 lbs?

25)  After sampling 300 parts, it was found that 8 were defective. At the 99% level of confidence, estimate the defect rate but forming a confidence interval.

26)  What contributions did the following people make: Galileo, Newton, Gauss, Faraday, Clerk Maxwell, Alan Turing, Robert Shockley, W.E.Deming

27)  If the mean number of arrivals to a terminal is 23/hour, what is the probability that in an hour there will be 25? Hint: use the Poisson distribution.

28)  If we draw and card from a standard deck, check to see if it is a king, then place it back in the deck and shuffle, what is the probability of getting 3 kings in five draws? (Hint: Binomial)

29)  What is the expected value of rolling a die? 