2:02 PM Fri Feb 3 Statistics Quiz Review Unit 6 Name: T Block: Direction: Read each question carefully, write neatly, easy to find solution. Show all work to receive any credit. Classify the following random variable according to whether it is discrete or continuous. 1. the number of bottles of juice sold in a cafeteria during lunch a. discrete b. continuous 2. the heights of the bookcases in a school library a. discrete b. continuous 3. the cost of a road atlas a. discrete b. continuous 4. the number of goals scored in a hockey game a. discrete b. continuous 5. the temperature in degrees Celsius on January 1st in Fargo, North Dakota a. discrete b. continuous 6. the time it takes to run a mile a. discrete b. continuous 7. the number of votes in an election a. discrete b. continuous + : 66% < -15 > 2:02 PM Fri Feb 3 T ... Statistics Quiz Review Unit 6 12. A student guesses at random on a multiple-choice quiz. There are 10 questions total with 4 choices and only one correct answer per question. The number of questions guessed correctly follows a Binomial distribution. a. What is the probability that the student answered 6 questions correct? b. What is the probability that the student answered at least 4 questions correct? c. What is the probability that the student answered at most 3 questions correct? d. What is the mean and standard deviation? + 66% 4 < 2:02 PM Fri Feb 3 5 T Statistics Quiz Review Unit 6 10. A family wants to have 4 children. Let X = the number of boys in the family. a. Complete the probability distribution table for X P(X = x) b. Using the table from part a, what is the expected value of X? c. Using the table from part a, what is the standard deviation of X? 11. A manufacturer produces many toasters. From experience, the manufacturer knows that approximately 5% are defective. In a quality control procedure, we randomly select 20 toasters for testing. Let X represent the number of defective toasters, which follows a Binomial Distribution. a. Determine the probability that exactly 2 of the toasters is defective. b. Find the probability that more than 4 of the toasters are defective. c. Find the probability that at least 3 of the toasters are defective. d. Find the mean and standard deviation of X. + : 66% 2:02 PM Fri Feb 3 5 Statistics Quiz Review Unit 6 T Formulas Expected Value (Mean) x = xi Pi Variance = p(xi - )2 Standard Deviation ox = Variance X Binomial (n, p) P(X = k) = binompdf(n,p,k) P(X k) = binomcdf(n,p,k) Mean & Standard Deviation: = = = np (1 p) + : 66% < 5 \5 > 2:02 PM Fri Feb 3 5 T Statistics Quiz Review Unit 6 8. The probability distribution gives the potential cost of routine maintenance and major repairs in the first 5 years you own a new car. Cost over 5 years Probability of cost $0 $500 $1,000 $1,500 $2,000 0.19 0.67 0.09 0.04 0.01 a. Find the expected value cost of routine maintenance and major repairs over the 5 years you own a new car. b. Find the variance and standard deviation for the cost of routine maintenance and major repairs in the first 5 years you own a new car. 9. A hundred tickets are sold for a movie at the cost of $10 each. Some tickets have cash prizes as a part of promotional campaign. One prize of $50, three prizes of $25, and five prizes of $20. The table below shows the probability distribution of X = Net win/loss for a single ticket purchase. x -$10 $20 $25 $50 P(X = x) a. What is the expected value of X? b. What is standard deviation of X? + : 66% < 215 >