Question 1. The following set of data gives exam scores in a class of 12 students. a) Sketch a box and whisker plot of the data.

Transcription

1 Question 1 The following set of data gives exam scores in a class of 12 students 25, 67, 86, 72, 97, 80, 86, 55, 68, 70, 81, 12 a) Sketch a box and whisker plot of the data. b) Determine the Interquartile Range c) Are there any outliers?

2 Question 1: Solution a) b) 22.5 = Exam Scores c) Yes, 12 and 25 because 12 < = = 61 (22.5)(1.5) and 25 < :30

3 Question 2 Determine the best measure of central tendency (mean, median, or mode) for each of the following: a) The typical size of dress sold in a store: b) The typical score on all homework assignments in a class (each homework assignment is worth the same): c) The typical cost of a piece of jewelry sold in a jewelry store:

4 Question 2: Solution a) The typical size of dress sold in a store: Mode b) The typical score on all homework assignments in a class (each homework assignment is worth the same): Mean c) The typical cost of a piece of jewelry sold in a jewelry store: Median 0 2:00

5 Question 3 The following chart represents the number of each color of marble in a bag. Draw a pie chart showing the colors. Show the size of each central angle to the nearest degree, label clearly. Color Number Blue 45 Brown 25 Green 19 Yellow 19 Red 30

6 Question 3: Solution Blue 117 Green 50 Brown 65 Yellow 50 Red 78

7 Question 4 Determine if the distributions of the following sets of data would most likely be normal (symmetric), skewed left, or skewed right: a) The number of siblings for each student in a class. b) The ages of people in a single parent family with 5 children under 10 years old. c) The weights of players on a baseball team.

8 Question 4: Solution a) The number of siblings for each student in a class. Skew Right b) The ages of people in a single parent family with 5 children under 10 years old. Skew Right c) The weights of players on a baseball team. Normal (Symmetric) 0 3:30

9 Question 5 Suppose you have a bag with Valentines Day candy. You have 10 red hearts, 5 black hearts, 3 chocolate hearts, 15 chocolate cupids, 10 red (cherry) cupids, 5 yellow peeps, and 10 red peeps. You reach in your bag and select a piece of candy at random. a) What is the probability that you will get a red candy? b) Let C be the event that the candy is a cupid, and R the event the candy is red. Find P (C R) and P (C R). c) What is the probability that you will get a chocolate or a heart? d) What are the odds in favor of selecting a cupid?

10 Question 5: Solution a) b) P (C R) = c) d) 25:33 and P (C R) = :30

11 Question 6 The odds a horse will win the race is 4:12. What is the probability the horse will win?

12 Question 6: Solution 4 16 = :30

13 Question 7 Consider the following bar chart showing the results of rolling a die. a) Is the graph symmetric, skewed left, or skewed right? b) What is the mean, median and mode of the data? 2 c) Would you consider this a fair die, explain Frequency Die Values

14 Question 7: Solution a) Skewed Right b) Mean = Median= 2 and Mode=2 c) No, a fair die would have all outcomes approximately equally likely. In this case, there were far more 1 s and 2 s than the other numbers and far fewer 6 s. 0 2:00

15 Question 8 Camille took a test where the mean score was 78 and the standard deviation was 5. If Camille s z-score on the test was -2.2, what was her score?

16 Question 8: Solution Let x = Camille s score. Then 2.2 = x = x = x 0 2:00

17 Question 9 If two people are selected at random, what is the probability that they are both born on April 26 th? (No leap year)

18 Question 9: Solution Well each person has a possible 365 birthdays, so there are a total of (365) 2 outcomes. Only one of these outcomes results in both of them having a birthday on April 26 th. So the probability is 1 (365) 2 = :00

19 Question 10 The mean score on Amy s ten quizzes was 8.9. If her lowest quiz was a 2, then what is her new average if she drops the lowest quiz score?

20 Question 10: Solution Let S = sum of Amy s ten quiz scores. Then 8.9 = S = S So, her new mean is S 2 9 = = :00

21 Question 11 Suppose the weights of 500 new born babies born in the Salem hospital during the Winter of last year formed an approximately normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. a) What percentage of the babies weighed between 6.25 and 10 pounds? b) What percentage of the babies weighed more than 10 pounds? c) 2.5% of babies weighed less than how many pounds? d) How many babies weighed between 7.5 and 10 pounds?

22 Question 11: Solution a) 81.8% because 6.25 is at 1σ and 10 is at +2σ b) 2.5% c) 5 lbs because 5 is at 2σ d) About 238 since (.475)(500) = :00

23 Question 12 Consider drawing 4 marbles from a jar without replacement. The jar contains 80 red, 70 purple, 100 green, and 15 blue marbles. a) What is the probability that you get a red then purple then red then green? b) What is the probability that you get a red, purple or green marble?

24 Question 12: Solution a) P(RPRG) = b) There are two ways one of which is really hard. Method I: Complement P(R, P, org) = 1 P(don t getr, P, org) = 1 P(all blue) = Method II: Addition Property P(R, P, org) = P(R) + P(P) + P(G) P(R P G) = (!!!!) The intersection is difficult to compute since RPGB is in there and so is PRGB, and GPRB, and RPRG, and GGRP, :30

25 Question 13 Alice, Bob, Carol, Denise, Ester, and Frank all put their names in a hat for being selected to get free concert tickets. Two names are selected at random to get the free tickets. a) Write down the sample space for the possible outcomes of selecting two names from the hat. b) What is the probability that Alice will be one of the two chosen? c) What is the probability that at least one boy will be chosen?

26 Question 13: Solution a) {AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF} b) c) 5 15 =

27 Question 14 In a group of 100 students who took calculus, the following grades were given: 20 As 40 Bs 40 Cs You wish to select a stratified sample of students from this class to ask their opinion of the course. If your sample is to contain 15 students, how many from each group will you pick?

28 Question 14: Solution 3 As 6 Bs 6 Cs

29 Question 15 Suppose the following graph shows the heights of mothers and fathers of students in a class. a) Is there a positive or negative correlation between the heights of fathers and mothers? b) Sketch a trend line on the graph and use it to estimate the height of a mother if the father were 67 inches tall.

30 Question 15: Solution a) Negative b) About 65 inches. Note: lines/answers will vary but should be similar

31 Question 16 A certain toy has a probability of failure of 0.4 (40% of all the toys don t work). Suppose you buy 5 of these toys. What is the probability that at least two of the 5 toys will fail? Estimate this probability by using the following table of randomly generated numbers from Explain your method and use at least 20 trials in your simulation sample

32 Question 16: Solution Since the probability of failure is 0.4 and the random numbers are from 1-10, I needed 4 numbers to represent toys that fail and 6 to represent toys that do not fail. I assigned the numbers 1-4 to represent failure and 5-10 to represent non-failure. All of the samples that have at least two defective toys are written in red. Random Samples Selected: 5, 5, 9, 6, 6 3, 2, 10, 6, 9 4, 8, 8, 6, 4 9, 9, 5, 3, 5 4, 10, 8, 3, 1 8, 3, 2, 7, 4 9, 8, 3, 3, 10 2, 5, 9, 5, 10 7, 4, 1, 5, 2 4, 9, 2, 6, 2 3, 4, 1, 9, 6 8, 10, 7, 9, 8 2, 5, 2, 10, 10 8, 4, 1, 10, 5 7, 6, 4, 1, 10 7, 7, 7, 5, 4 4, 1, 10, 6, 6 9, 8, 7, 6, 6 4, 1, 7, 6, 1 8, 9, 1, 4, 1 So the (experimental) probability is = 4 5 = 0.8. Note: Answers will vary but should be similar. Also, doing something similar on your calculator is acceptable; as always, just be sure to explain your process.