14 CHAPTER 3. DATA DESCRIPTION. Math 150 Homework For the following data: 4, 4, 5, 6, 6, 7, 7, 7, 10, 12, 16 find the

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1 14 CHAPTER 3. DATA DESCRIPTION Math 150 Homework 3.1 Name: Date: 1.- For the following data: 1.3, 1.7, 2.1, 2.5, 2.8, 3.7, 3.7, 4.1, 4.3, 4.4, 5.5 find the Mean Median Mode (d) Midrange 2.- For the following data: 4, 4, 5, 6, 6, 7, 7, 7, 10, 12, 16 find the Mean Median Mode (d) Midrange

2 3.1. MEASURES OF CENTRAL TENDENCY Find the mean and modal class for the following. Class limits Frecuency Class limits Frecuency For the following data set 10, 7, 6, k, 4, 7, 1, 10. Find the value of k so that X = 6.25 X = 7.5

3 16 CHAPTER 3. DATA DESCRIPTION M = 7 (d) MR = 10 True/False For any given data set X, M, and X can NOT be the same. X divides an ascending data set into two equal parts. X is always bigger than X. (d) For any given data set X = MR.

4 3.2. MEASURES OF VARIATION 19 Math 150 Homework 3.2 Name: Date: 1.- For the following data set 2, 3, 3, 4, 4, 5, 6, 7 find the Variance Standard deviation Coefficient of Variation 2.- For the following data 1.2, 1.3, 2.2, find the Variance Standard deviation Coefficient of Variation 3.- Which data set is more variable, the data set for question #1 or the data set for question #2? Explain.

5 20 CHAPTER 3. DATA DESCRIPTION 4.- Find the variance and standard deviation. Class limits Frecuency True/False For any random sample S 2 > S For any random sample S 2 0 If S 2 = 0 then CV = 0 (d) The empirical rule contradicts Chevychev s theorem.

6 26 CHAPTER 3. DATA DESCRIPTION Math 150 Homework 3.3 Name: Date: 1.- For the following data: 1.3, 1.7, 2.1, 2.5, 2.8, 3.7, 3.7, 4.1, 4.3, 4.4, 5.5 find the FIVE NUMBER summary P 67 Draw a boxplot (whisker box) 2.- For the following data: 10, 10, 30, 35, 45, 55, 65, 75, 75, 80, 80, 90, 100 find the FIVE NUMBER summary P 35

7 3.3. MEASURES OF POSITION 27 Draw a boxplot (whisker box) 3.- Find the outliers (if any) in the following data set: 1, 7, 8, 8, 9, 10, 10, 10, 12, 18, 25, 27, 30 True/False For any random sample X = Q 2 For any random sample X = P 50 For any random sample P 25 > Q 1 (d) P 75 is NOT part of the FIVE NUMBER summary (e) IQR = Q 1 + Q 3

8 32 CHAPTER 4. PROBABILITY Math 150 Homework 4.1 Name: Date: 1.- If a die is rolled one time, find the following probabilities. Of getting a 6 Of getting a number less than 4 Of getting a 1 or a 5 (d) Of getting an even number 2.- If a die is rolled twice, find the following probabilities. Of getting a sum of 12 Of getting a sum of 7 Of getting a sum of less than 5 (d) Of getting a sum of more than 9

9 4.1. PROBABILITY BASICS 33 (e) Of getting a sum of 1 Use a tree-diagram to find the following probabilities. 3.- A multiple choice test has 3 questions and each question has 3 choices. If Nacho takes this test, what is the probability that he will: answer all questions correctly? answer all questions wrong? answer two questions correctly? 3.- A test has two true/false questions and two multiple choice questions. Each multiple choice question has 3 choices. If Barney takes this test, what is the probability that he will answer all questions correctly?

10 34 CHAPTER 4. PROBABILITY answer all questions wrong? True/False For any event A if P (A) = 0 then event A will never happen. If P (A) = 1 then event A is guarantee to happen. For any event E, P (E) + P (E) = 1

11 36 CHAPTER 4. PROBABILITY Math 150 Homework 4.2 Name: Date: students at ECC-CC were asked about their eating preferences. The following table summarizes the results. Table 4.1: Eating preferences - Vegetarian Carnivorous Omnivorous Male Female What is the probability that a randomly selected student is Vegetarian? What is the probability that a randomly selected student is NOT female? What is the probability that a randomly selected student is Male or Omnivorous? (d) What is the probability that a randomly selected student is Vegetarian or Carnivorous? 2.- A math 150 class has 45 students. 26 of the students are Lakers fans, 20 are Dodgers fans, and 10 are both. What is the probability that a randomly selected student will be: either a Lakers or a Dodgers fan?

12 4.2. ADDITION RULE 37 NOT a Dodgers fan? a Lakers fan but NOT a Dodgers fan? (d) neither a Lakers fan or a Dodgers fan? 3. The probability that a student owns a computer is 0.46, and the probability that a student owns a smart-phone is If the probability that the student owns both is What is the probability that a randomly selected student will: own either a computer or a smart-phone? own neither a computer or a smart-phone? own a computer but NOT own a smart-phone?

13 38 CHAPTER 4. PROBABILITY (d) own a smart-phone but NOT own a computer? 4.- Use the below contingency table to find the following probabilities. - Republican Democrat Libertarian Christian Muslim Jews What is the probability that a randomly selected person is either Republican or Muslim? What is the probability that a randomly selected person is either Democrat or NOT a muslim? What is the probability that a randomly selected person is NOT Christian or NOT Libertarian? True/False If A and B are mutually exclusive then P (A B) = 1 If P (A) = 0.33 then P (A) = 0.77 For any event A, P (A) > 0 (d) For any two events A and B, P (A B) P (B)

14 40 CHAPTER 4. PROBABILITY Math 150 Homework 4.3 Name: Date: 1.- According to a local survey 76% of Angelinos are Lakers fans. If you randomly select five Angelinos: what is the probability that are all Lakers fans? what is the probability that none of them are Lakers fans? what is the probability that one is a Lakers fan? 2.- If you flip a coin and throw two dice at the same time, what is the probability that you will get a face and two 4 s? 3.- Mickey rats goes to Target and buys two alarm clocks. The probability that any of the alarms will fail on any given day is 1%. What is the probability that both of them will work next Friday? What is the probability that both of them will fail next Friday?

15 4.3. INDEPENDENCE AND CONDITIONAL PROBABILITY 41 What is the probability that the alarms will wake him up next Friday? (d) What is the percent increase in reliability by having two alarms as compared to one? students at ECC-CC were asked about their eating preferences. The following table summarizes the results. Table 4.2: Eating Preferences - Vegetarian Carnivorous Omnivorous Male Female If a student is randomly selected, what is the probability: given that student is male that he is Vegetarian? given that student is female that she is Carnivorous? Are Male and Carnivorous independent events? 5.- Suppose 40% of college students live with their parents, 65% have a part-time job, and 26% live with their parents and have a part-time job. Are the events living with their parents and have a part-time job independent? Explain.

16 42 CHAPTER 4. PROBABILITY 6.- Consider the following probabilities: P (A) = 0.4, P (B) = 0.5. If A B, find P (A B) P (A B) P (B A) (d) P (A B) (e) P (A B) 7.- Suppose that P (A) = 0.2, P (B) = 0.3, and P (A B) = 0.06 find P (A B) P (B A) Are A and B independent? Explain

17 44 CHAPTER 4. PROBABILITY Math 150 Homework 4.4 Name: Date: 1.- Social security numbers consist of nine digits (which can be repeated). How many different choices are there for social security numbers? What is the probability that you will guess Obama s social security number correctly in your first guess? 2.- The simple Passcode for an iphone consists of four digits (which can be repeated). How many different simple Passcodes are there for any iphone? If your boyfriend has an iphone with a Passcode on it, what is the probability that you will guess the correct Passcode in the first try? Your boyfriend has set the Passcode so that after three failed attempts the iphone locks. What is the probability of this happening? 3.- Batman, Barney, Mikey Rats, Nacho, and the Chupacabra compete in a 100 meters race. Assuming no ties, how many different outcomes are there for the race?

18 4.4. COUNTING 45 What is the probability that Barney wins the race? What is the probability that Barney wins, Batman gets second place, and Nacho gets the third place? 4.- If you pick five cards from a standard 52-deck, what is the probability of getting two kings and three 4s? what is the probability of getting four s and one? what is the probability of getting three aces? (d) what is the probability of getting two s and two s?

19 46 CHAPTER 4. PROBABILITY 5.- An international Math 150 class has 5 African students, 4 European students, 8 American students, and 7 Asian students. In how many ways can a president, a vice-president, and a secretary be chosen? What is the probability that the president will be American, the vice-president Asian, and the secretary African? What is the probability that the president, vice-president, and secretary will be American? True/False For any whole number n, n! = n(n 1)! For any two whole numbers n and k, n C k = n P k k! For any whole number n, n C 0 = 1 (d) For any whole number n, n C 1 = n

20 48 CHAPTER 4. PROBABILITY Math 150 Homework 4.5 Name: Date: 1.- Apple has two factories producing iphones. Factory I produces 40% of the iphones while Factory II produces the remaining iphones. 1% of iphones produced by Factory I are defective while 2% of iphones produced by Factory II are defective. If you buy and iphone, What is the probability that it will be defective? What is the probability that it will be non-defective? If the phone is defective, what is the probability that it come from Factory II? 2.- Suppose that 45% of the population is male and that 12% are smokers. If 8% of females are smokers, what is the probability that A randomly selected person is a smoker?

21 4.5. BAYE S RULE 49 A randomly selected person is NOT a smoker? If the person selected was a smoker, that the person was male? 3.- Two percent of the USA population suffers from the Donald Duck s disease. The Center for Disease Control has a test to diagnose for this disease. The test is 99% effective if the person has the disease and 98% effective if the person does not have the disease. What is the probability that a randomly selected person taking the test: will have a Positive result? will have a Negative result? Given that the person tested positive, what is the probability that he/she actually is infected with this disease?

22 50 CHAPTER 4. PROBABILITY 4.- Barney has two boxes with marbles inside. Box 1 contains six red marbles and three green marbles. Box 2 contains four red marbles and five green marbles. He is going to play the following game: Pick (randomly) a marble from Box 1 and put it in Box 2. Then mix the marbles in Box 2 and randomly pick another marble. What is the probability that the second marble is red? What is the probability that the second marble is green? If the second marble was red what is the probability that the first marble was green?

23 Appendix A Solutions to Homework Problems Section x = 3.3, x = 3.7, M = 3.7, MR = x = 7.6, x = 7, M = 7, MR = x gd = 21.6 x gd = 73.5 True/False False True False (d) False Section S 2 = 2.8, S = 1.7, CV = 40% 2.- S 2 = 1.9, S = 1.4, CV = 56% 3.- Question 2 because the CV is bigger 4.- Sgd 2 = 125.9, S gd = True/False False True True (d) False Section L = 1.3, Q 1 = 2.1, Q 2 = 3.7, Q 3 = 4.3, H = 5.5 P 67 = L = 10, Q 1 = 35, Q 2 = 65, Q 3 = 80, H = 100 P 35 = No outliers. True/False True True False (d) False (e) False