Worksheet 5 (Ch. 5) copy

Worksheet 5 – Elementary Sta 3 s 3 cal Methods Names: ___________________________________________________ 1. Determine whether the distribution represents a probability distribution. If it does not, state why. a. b. c. 2. Mathematics Tutoring Center. At a drop-in mathematics tutoring center, each teacher sees 5 to 9 students per hour. The probability that a tutor sees 5 students in an hour is 0.107; 6 students, 0.125; 7 students, 0.298; and 9 students, 0.342. Find the probability that a tutor sees 8 students in an hour and construct the probability distribution. Probability of 8 students = 1 - (0.107 + 0.125 + 0.298 + 0.342) Probability of 8 students = 0.128 Probability of 5 students = 0.107 Probability of 6 students = 0.125 Probability of 7 students = 0.298 Probability of 8 students = 0.128 Probability of 9 students = 0.342 X 1 5 1 6 2 0 25 P(X ) 0. 6 0. 5 0. 7 − 0. 8 X − 5 − 3 0 2 4 P(X ) 0. 1 0. 3 0. 1 0. 3 0. 1 X 20 30 4 0 5 0 P(X ) 0.0 5 0.3 5 0. 4 0. 2

3. Traffic Accidents. The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. Find the mean, variance, and standard deviation. 4. Benford’s Law The leading digits in actual data, such as stock prices, population numbers, death rates, and lengths of rivers, do not occur randomly as one might suppose, but instead follow a distribution according to Benford’s law. Below is the probability distribution for the leading digits in real-life lists of data. Calculate the mean, variance, and standard deviation. for the distribution. 5. Dice Game. A person pays $3 to play a certain game by rolling a single die once. If a 1, 2, or 3 comes up, the person wins nothing. If, however, the player rolls a 4, 5, or 6, she or he wins the difference between the number rolled and $3. Find the expectation for this game. Is the game fair? For rolling a 1, 2, or 3: Expected winnings = (3/6) * $0 = $0 N umber of accidents X 0 1 2 3 4 Probability P(X ) 0.3 1 0.1 8 0.1 7 0.1 5 0.1 9 X 1 2 3 4 5 6 7 8 9 P(X ) 0.20 1 0.07 0 0.12 5 0.18 7 0.17 9 0.07 7 0.04 8 0.05 7 0.05 6

9. Watching Fireworks. A survey found that 37% of Americans watched fireworks on television on July 4, 2020. Find the mean, variance, and standard deviation of the number of individuals who watch fireworks on television on that day if a random sample of 2200 Americans is selected. The mean number of individuals who watch fireworks on television in a random sample of 2200 Americans is 814. The variance of the number of individuals who watch fireworks on television is approximately 517.74, and the standard deviation is approximately. 10. Alternate Sources of Fuel. Seventy-seven percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 215 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels. The mean number of Americans who favor government spending on alternative fuels in a random sample of 215 is approximately 165.55. The variance of the number of Americans who favor government spending on alternative fuels is approximately 38.1855, and the standard deviation is approximately 6.18.