& Statistics Practice Quiz - Distributions Name: Date: Answer the questions. For each question, state the method you used. Sketch the graph that corresponds to the probability you are finding. (You can copy a quick sketch of the Minitab output.) 1. The two types of probability distributions we studied are and. 2. Which of the following variables are discrete? i. the depth of a submarine ii. the number of torpedoes on a submarine iii. the speed of the submarine A) ii B) i and iii C) i and ii D) i, ii, and iii 3. Which of the following variables are continuous? i. an automobile's gas mileage ii. the air pressure in an automobile's spare tire iii. an automobile's sticker price A) None are continuous. B) i C) i and ii D) i, ii, and iii 4. The following distribution is not a probability distribution because 2 1 0 1 2 P() 0.13 0.21 0.42 0.12 0.29 A) the values of the variable are negative. B) the probability values are not increasing. C) the probability values do not add to 1. D) the probability values are not discrete. 5. The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for these data. Number of calls 8 9 10 11 12 P() 0.21 0.31 0.16 0.14 0.18 Page 1
6. Using the probability distribution listed, the mean would be 1.6. 0 1 2 3 P() 0.2 0.1 0.3 0.4 A) True B) False. The true mean is. 7. If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts? 8. In a survey, 55% of the voters support a particular referendum. If 30 voters are chosen at random, find the probability that 20 or more of them support the referendum. 9. The probability of a success remains the same for each trial in a binomial experiment. A) True B) False 10. A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries. 11. A student takes a 10-question, multiple-choice exam with three choices for each question and guesses on each question. Find the probability of guessing exactly 2 out of 10 correctly. 12. In a batch of 100 cell phones, there are, on average, 9 defective ones. If a random sample of 30 is selected, find the probability of 3 defective ones. 13. The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? 14. If a baseball player's batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat? Page 2
15. A biologist estimates that 80% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 246 or fewer deer have this tick? 16. A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving. 17. Find the area under the standard normal distribution curve to the left of z = 1.69. 18. If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50. Page 3
Answer Key 1. Discrete/Binomial and continuous/normal 2. A 3. C (Sticker price is usually given in increments of $1000.) 4. C 5. 6. B; 1.9 7. 00 0.25 Binomial, n=200, p=0.015 002 8. 0.1350 0 6 9 Binomial, n=30, p=0.55 0.16 0.14 0.12 0.08 0.1350 8 20 9. A 10. 0.8760 Binomial, n=1000, p=5 0.8760 0 3 Page 4
Density 11. 0.1951 Binomial, n=10, p=0.3333 0.25 0.1951 12. 0.2319 0 2 8 Binomial, n=30, p=0.09 0.25 0.2319 13. 0.2893 0 3 8 Normal, Mean=6.5, StDev=0.45 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.2893 0.1 0.0 14. 0.131 6.5 6.75 Binomial, n=200, p=0.34 0.03 0.01 0.1310 60 90 Page 5
Density 15. 0.8255 Binomial, n=300, p=0.8 0.03 0.8255 0.01 246 261 16. 0.0131 Binomial, n=500, p= 0.08 0.07 0.03 0.01 17. 0.9545 0.01306 14 40 48 18. 4.8% 0.035 Normal, Mean=70, StDev=12 0.030 5 0 0.015 0.010 5 779 0 50 70 Page 6