1. (9; 3ea) The table lists the survey results of 100 non-senior students. Math major Art major Biology major
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1 Math 54 Test #2(Chapter 4, 5, 6, 7) Name: Show all necessary work for full credit. You may use graphing calculators for your calculation, but you must show all detail and use the proper notations. Total is 100 points. 1. (9; 3ea) The table lists the survey results of 100 non-senior students. Math major Art major Biology major Freshman Sophomore Junior If a student is chosen at random, find the probability of getting someone: a. Who is a sophomore. b. Who is a sophomore or a math major c. Who is a freshman with biology major? 2. (6) Exclude leap years. a. Determine the probability that a randomly selected person has birthday on the 8 th of a month. b. Determine the probability that a randomly selected person does not have birthday in September. 1
2 3. (12) Use the standard normal distribution table to find the following. For each, draw the diagram (density curve). a. P ( Z 1.27) P 0.80 Z 2.08 c. ( ) b. P ( Z > 0.56) d. ( Z > k) = P, find k. 4. (12) A survey shows that 75% of customers will order a pizza at a restaurant. Suppose 12 customers are randomly selected. a. Find the probability that exactly 7 of them are ordering pizza. b. Find the probability that at least 6 of them are ordering pizza. c. Find the mean and standard deviation of the random variable. Would it be unusual if only 5 customers order pizza? Explain. 2
3 5. (5) Men s heights are normally distributed with a mean 69.0 in and standard deviation of 2.8 in. What percentage of men is taller than 72 in.? 6. (5) The scores of a final exam in Mat54 class are normally distributed with a mean of 73 and standard deviation of 7.8. If one student is randomly selected, find the probability that the student has a score greater than (5) Birth weights in the United States are normally distributed with a mean of 3420 g and standard deviation of 495 g. If a hospital plans to set up special observation condition for the lightest 2% of babies, what weight is used for the cutoff separating the lightest 2% from the others? 3
4 8. (6) A survey shows that 45% of the adults said that they used the Internet for shopping at least a few times a year. If 450 adults are randomly selected, estimate the probability that at least 230 of them used the Internet for shopping at least few times a year. (Use normal distribution as approximation the binomial distribution). 9. (6) For a group of four men, the probability distribution for the number x who live through the next year is give in the table. Find the mean and the standard deviation for the probability distribution. X P(x) (5) The random-number generator on calculator randomly generates a number between 0 and 1 The random variable X, the number generated, follows a uniform probability distribution. Draw the graph of the uniform density function, then find the probability of generating a number between 0.25 and 0.6? 4
5 11. (12)A pediatrician wants to determine the relation that may exist between a child s height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in the table below. X = height (inches) Y = head circumference (inches) a. Calculate the linear correlation coefficient, r, and interpret it. b. Test whether there is a linear relationship between the a child s height and head circumference ( Find the critical value and compare with r ) c. Find the regression equation. Interpret the meaning of the slope and the y-intercept, if appropriate. d. Use the regression equation to predict the head circumference of a child who is 25 inches tall. 5
6 12. (6) Are you more likely to be satisfied with your automobile purchase when it is new or used? The following data represent the level of satisfaction of the buyer for both new and used cars. New Used Not too satisfied Pretty satisfied Extremely satisfied a. How many were extremely satisfied with their automobile purchases? b. What proportion of consumers was extremely satisfied with their automobile purchase? 13. (2, 3) About 13% of the population is left-handed. a. What is the probability that a randomly selected person is not left-handed? b. If three people are randomly selected, what is the probability that all three are left-handed? 14. (6) Find the value of Z α Z b. Z a
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