STAT 200 6388MID-TERM Exam September 2019Instructor: E. Avram NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone. INSTRUCTIONS The quiz is worth 100 points. There are 10 problems.This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone. You may take as much time as you wish, provided you turn in your quiz work no later than Monday, September 23, 2019, 11:59 pm. Show work/explanation unless specified otherwise. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work (the sentence under “Name” at the beginning of the quiz) A statistics class has the following activities and weights for determining a grade in the course: test 1 worth 15% of the grade, test 2 worth 15% of the grade, test 3 worth 15% of the grade, homework worth 10% of the grade, semester project worth 20% of the grade, and the final exam worth 25% of the grade. If a student receives a 92 on test 1, an 85 on test 2, a 95 on test 3, a 92 on the homework, a 55 on the project, and an 83 on the final, what grade did the student earn in the course? (Section 3.1)The time (in 1/50 seconds) between successive pulses along a nerve fiber (“Time between nerve,” 2013) are given in table #3.2.20. Table 3.2.20: Time (in 1/50 seconds) Between Successive Pulses 10.5 1.5 2.5 5.5 29.5 3 9 27.5 18.5 4.5 7 9.5 1 7 4.5 2.5 7.5 11.5 7.5 4 12 8 3 5.5 7.5 4.5 1.5 10.5 1 7 12 14.5 8 3.5 3.5 2 1 7.5 6 13 7.5 16.5 3 25.5 5.5 14 18 7 27.5 14 a.) Using technology, find the mean and standard deviation. b.) Use Chebyshev’s theorem to find an interval centered about the mean time between successive pulses along a nerve fiber in which you would expect at least 75% of the times to fall. c.) Use Chebyshev’s theorem to find an interval centered about the mean time between successive pulses along a nerve fiber in which you would expect at least 88.9% of the times to fall. (Section 3.2) 3. An experiment is rolling a fair die and then flipping a fair coin. a.) State the sample space. b.) Find the probability of getting a head. Make sure you state the event space. c.) Find the probability of getting a 6. Make sure you state the event space. d.) Find the probability of getting a 6 or a head. (Section 4.2) 4. An experiment is pulling a ball from an urn that contains 3 blue balls and 5 red balls. a.) Find the probability of getting a red ball. b.) Find the probability of getting a blue ball. c.) Find the odds for getting a red ball. (Section 4.2) 5.You are opening a T-shirt store. You can have long sleeves or short sleeves, three different colors, five different designs, and four different sizes. How many different shirts can you make (Section 4.4) 6. The Ohio lottery has a game called Pick 4 where a player pays $1 and picks a four-digit number. If the four numbers come up in the order you picked, then you win $2,500. What is your expected value? (Section 5.1) 7. Suppose a random variable, x, arises from a binomial experiment. If n = 22, and p= 0.85, find the following probabilities using the binomial formula. (Section 5.2) a.) P (x = 18) b.) P (x £ 3) c.) P (x ³ 18) 8. Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 16.9% defective lenses due to scratches. Suppose Eyeglassomatic examined twenty eyeglasses (Section 5.3) a.) State the random variable. b.) Write the probability distribution. e.) Find the mean. 9. Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of m = 0 and standard deviation o = 1. a.) The area to the left of z is 15%. b.) The area to the right of z is 65%. c.) The area to the left of z is 10%. 10.In the United States, males between the ages of 40 and 49 eat on average 103.1 g of fat every day with a standard deviation of 4.32 g (“What we eat,” 2012).Assume that the amount of fat a person eats is normally distributed. a.) State the random variable. b.) Find the probability that a man age 40-49 in the U.S. eats more than 110 g of fat every day. c.) Find the probability that a man age 40-49 in the U.S. eats less than 93 g of fat every day. d.) Find the probability that a man age 40-49 in the U.S. eats less than 65 g of fat every day. (Section 6.3.)
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