Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103 1. (8) The following are amounts of time (minutes) spent on hygiene and grooming in the morning by survey respondents. 4 6 7 9 14 15 15 16 18 18 25 26 30 32 41 45 55 63 a. List the five number summary. b. Is there any outlier (use the IQR method to determine this)? If so, list it. Then construct a box plot. 2. (12) The Department of Agriculture reports that the mean consumption of carbonated beverages per year per American is greater than 52 gallons. A sample of 30 Americans yielded a sample mean of 60 gallons and a standard deviation of 35 gallons. a. Assume that the distribution is bell-shaped, estimate the proportion of Americans who drink between 25 and 95 gallons per year. b. Assume that the distribution is bell-shaped, find the 2.5 th percentile. c. Assume that the distribution is unknown, estimate the proportion of Americans who drink between 4 and 116. 1
3. (9) Consider the experiment of rolling a fair die twice. Find the following probabilities. a. Sum of the two dice equals 6 or 10. b. Exactly one of the dice shows 6. c. Sum of the two dice equals 6 and neither of the dice is a 4. 4. (8) Consider the experiment of drawing a single card from a deck of 52 cards. Find the probability of drawing a a. Card that is not a diamond. b. Face card (king, queen, or jack) c. A face card or a diamond d. Face card and a diamond 2
5. (9) Color preference and gender Gender Pink Blue Female 40 60 Male 10 90 A person is randomly selected, find the following probabilities a. that person prefers pink b. that person prefers pink or is a female. c. that person is a male and prefers blue 6. (9) Your sister is going to have triplets. Assume that the probability of a baby boy or baby girl is equally likely. a. Construct a sample space. b. Find the probability of 1 girl or 1 boy. c. Find the probability of at least 2 girls. 3
7. (16)The table below lists weights (carats) and price (dollars) of randomly selected one type of diamonds. X = Weight Y = price 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 a. Find r and 2 r. Brief explain the meaning for each number. b. Test whether there is a linear relationship between the weights and the prices of diamonds (Compare r with the critical value from table G) c. Find the regression equation. Interpret the meaning of the slope and the y-intercept. d. Estimate the price of the same type of diamond with weights 0.6 carats. 4
8. (10) A sociologist randomly selects single adults for different groups of four, and the random variable X is the number adults in the group who say that the most fun way to flirt is in person. X P(x) 0 0.042 1 0.200 2 0.367 3 0.299 4 0.092 a. (2)Determine whether the distribution represent a valid probability distribution. Explain b. (2) Find P(X 2) c. (3) Find the mean and standard deviation. d. (3) Convert X = 4 to z-value. Would it be unusual if all 4 adults say that the most fun way to flirt is in person? 9. (4) Determine whether the experiment is binomial or not. If the experiment is binomial, identify the random variable X, the number of trials n, the probability of success p, and the probability of failure q. If the experiment is not binomial, explain why not. Answer a random sample of 8 multiple-choice questions either correctly or incorrectly by random guessing. There are 4 choices (A, B, C, D), for each question. 5
10. (18) Based on a poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that twelve adults who regret getting tattoos are randomly selected, and find the indicated probability. a. For this binomial experiment, identify the random variable X, the number of trials n, the probability of success p, and the probability of failure q. b. Find the probability that none of the selected adults say that they were too young to get tattoos. c. Find the probability that exactly three of the selected adults says that he or she was too young to get tattoos. d. Find the probability that at most three of selected adults saying they were too young to get tattoos. e. Find the probability that at least three of selected adults saying they were too young to get tattoos. f. Find the mean and the standard deviation of the number of adults say they were too young to get tattoos. 6