1. Two hundred students took a standard chemistry test. You sampled 20 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation? (1 POINT) a. 21 b. 20 c. 19 d. 40 2. Which of the following descriptions of \"bias\" is correct? (Select all that apply) (1 POINT) a. A sampling method is biased if each element does not have an equal chance of being selected. b. A sampling method is biased if every element is selected c. An estimator is biased if it systematically overestimates or underestimates the parameter it is estimating d. An estimator is biased if it overestimates but does not underestimates the parameter 3.The t distribution becomes closer to a normal distribution when the degrees of freedom___. (1 POINT) a. Increase b. Decrease c. First Increase and then decrease d. First decrease and then increase 4. (Show work) In a bag of peanut M & M's, there are 80 M & Ms, with 11 red ones, 12 orange ones, 20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They are mixed up so that each candy piece is equally likely to be selected if we pick one. (10 POINTS) (a) If we select one at random, what is the probability that it is red? (b) If we select one at random, what is the probability that it is not blue? (c) If we select one at random, what is the probability that it is blue or green? (d) If we select one at random, then put it back, mix them up well and select another one, what is the probability that both the first and second ones are blue? (e) If we select one, keep it, and then select a second one, what is the probability that the first one is yellow and the second one is blue? 5. (Show work) Suppose that 35% of all patients admitted to a hospital's intensive care unit have high blood pressure, 42% have some sort of infection, and 12% have both problems. Probabilities estimated from the data in ICU Admissions. (10POINTS) (a) Find the probability that a randomly chosen patient in this ICU has either high blood pressure or an infection. (b) Find the probability that a patient admitted to the ICU has high blood pressure given that an infection is present. 6. (Show work) A company manufactures light bulbs with a mean life of 500 hours and a standard deviation of 100 hours. If it is assumed that the useful lifetimes of the light bulbs are normally distributed, find the number of bulbs out of 10000 that can be expected to last between 650 and 780 hours. (6POINTS) 7. (Show work) The heights of adult males are normally distributed with a mean of 70 inches and a standard deviation of 2.6 inches. How high a doorway should be constructed so that 90% of the men can pass through it without having a bend? (6POINTS) 8. (Show work) Suppose that the hourly wages of all workers in certain auto plant are normally distributed with a mean of 12.50 and a standard deviation of $0.95. If a random sample of 100 workers is selected from this plant find the probability that the sample mean hourly wage is (10 POINTS) (a) Between $12.45 and $12.65 (b) More than $12.30 9. (Show work) A researcher wanted to know the percentage of the urban population that had ever experienced depression in the past month. He randomly sampled 500 adults in a big city. He found that 20 percent of them had experienced any type of depression in the past month. What's the upper limit of 95% of the confidence interval (as proportion)? (5 POINTS) 10. (Show work) Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean surveyed deviation amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard of four hours. (10POINTS) (a) Which distribution should you use for this problem? Explain your choice. (b) Construct a 99% confidence interval for the population mean length of time using training wheels. State the confidence interval. (c) Sketch the graph. (d) Explain in a complete sentence what the confidence interval means in this problem. 10. (Show work) Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean surveyed deviation amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard of four hours. (10POINTS) (a) Which distribution should you use for this problem? Explain your choice. (b) Construct a 99% confidence interval for the population mean length of time using training wheels. State the confidence interval. (c) Sketch the graph. (d) Explain in a complete sentence what the confidence interval means in this