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- 1. Math 221 Quiz Review for Weeks 3 and 4 1. State whether the variable is discrete or continuous. The # of keys on each student's key chain. 2. Decide whether the experiment is a binomial experiment. Explain why by citing the properties of binomial experiments. Testing a pain reliever using 20 people to determine if it is effective. The random variable represents the number of people who find the pain reliever to be effective. 3. Use the binomial probability distribution to answer the following probability questions. According to government data, the probability that an adult under 35 was never married is 25%. In a random survey of 10 adults under 35, what is the probability that: Exactly 5 were never married? 4. Use the binomial probability distribution to answer the following probability questions. According to government data, the probability that an adult under 35 was never married is 25%. In a random survey of 10 adults under 35, what is the probability that: No more than two were never married? 5. True or False: Given the basic rules of Probability, P(A) can be equal to negative 0.18 or - 18%. 6. We have the random variable X = {3, 6} with P(3) = .15 and P(6) = .85. Find E(X). 7. Use the binomial probability distribution to answer the following probability questions. According to government data, the probability that an adult under 35 was never married is 25%. In a random survey of 10 adults under 35, what is the probability that: Between 4 and 6 were never married (inclusive)? 8. Use the Poisson probability table in the back of your text to answer the following probability questions. Amazon.com receives an average of 5 sales per second through their Internet site. What is the probability that: They will get exactly 8 sales during the next second?
- 2. 9. We have a Poisson distribution with mean = 3. Find P(X = 2), P(X < 2), find P(X <= 2), P(X > 2), the variance, and standard deviation. 10. How many ways can a committee of 7 be chosen from 20 people? 11. State whether the variable is discrete or continuous. The blood pressure readings of a group of students the day before their final exam. 12. Use this table to answer the question below. Some students were asked if they carry a credit card. Here are the responses. Class____________ | Credit Card Carrier | Not a Credit Card Carrier | Total Freshman________________30____________________32____________62 Sophomore________________7____________________31____________38 Total____________________37____________________63____________100 What is the probability that the student was a freshman? 13. Use this table to answer the question below. Some students were asked if they carry a credit card. Here are the responses. Class____________ | Credit Card Carrier | Not a Credit Card Carrier | Total Freshman________________30____________________32____________62 Sophomore________________7____________________31____________38 Total____________________37____________________63____________100 What is the probability that the student is a freshman and carries a credit card? 14. If there are 25 members in a club, in how many different ways can you select people to serve on a committe of 3 people? 15. If there are 25 members in a club, in how many different ways can you select the president, the secretary and the treasurer. 16. List the sample space of rolling a 9 sided die. 17. How many different license plates can be made if they have 2 numerical digits followed by 5 letters and there are no other restrictions? 18. If P (A) = 0.65 or 65%, what is the value of P (not A)?
- 3. 19. A class has 17 women and 15 men. If a student if chosen randomly, what is the probability the student is a woman? 20. Compute the following and show your steps. 7! / 5!. 21. We have a binomial experiment with p = .3 and n = 2. (1) Set up the probability distribution by showing all x values and their associated probabilities. (2) Compute the mean, variance, and standard deviation. 22. Yes or No: Suppose X = {1, 2, 3, 4} and P(1) = .3, P(2) = .5, P(3) = .1 and P(4) = .2. Can the distribution of the random variable X be considered a probability distribution? 23. The Student Services office did a survey of 300 students in which they asked if the student is part-time or full-time. Another question asked whether the student was a transfer student. The results follow. Transfer Non-Transfer Row Totals Part-Time 160 20 180 Full-Time 30 90 120 Column Totals 190 110 300 Show answers as fractions (e.g., 25/150) and show your work. If a student is selected at random (from this group of 300 students), find the probability that The student is a transfer student. P (Transfer) 24. Decide whether the experiment is a binomial, Poisson or neither based on the info given. A book contains 500 pages. There are 200 typing errors randomly distributed throughout the book. We're interested in knowing the probablity that a certain page contains an error.
- 4. Answer Key 1. Because you can count the number of keys and this is an integer value, this is discrete data. 2. Yes, this is a binomial. The pain reliever is either effective or ineffective on each dose (trial). The probability of it working is the same on every trial, so this would be a legitimate binomial probability experiment. 3. P (5) = .058 Feedback: binompdf(n, p, x) is binompdf(10, 0.25, 5) 4. P (x < 3) = P(0) + P(1) + P(2) = ..056 +.188 + .282 = .526 Feedback: binomcdf(10, 0.25, 3) 5. False Feedback: The probability of any event can never be less than 0. 6. E(X) = sum of (x*P(X)) = 3*P(3) + 6*P(6) = 3*.15 + 6*.85 = .45 + 5.1 = 5.55 7. P (4 <= x <= 6) = P(4) + P(5) + P(6) = .146 + .058 +.016 = .220 8. P (8) = .0652... 9. P(X = 2) = .224 P(X < 2) = .199 P(X <= 2) = .423 P(X > 2) = 1 - .423 = .577 mean = variance = 3 standard deviation = sqrt(variance) = 1.732 10. Use the formula nCr because order doesn't matter: 20 C 7 = 77520. 11. Blood pressure readings are measured on a continuous scale. BP can take on any value on the number line and measured with fine precision. 12. P(Freshman) = 62/100 = .620 13. P(Freshman AND Credit Card Carrier) = 30/100 = .300
- 5. 14. Since order doesn't matter, this is a combination. nCr = n!/{(n-r)!*(r)!} Since there are 25 members and we want a committee of 3, we have 25C3 = 25! ÷ {(25 -3)!*(3)!} = 25! ÷ {22!*3!} =25*24*23*22! ÷{ 22! * 3*2*1} = 25*24*23 ÷ 3*2*1 =13800 ÷ 6 = 2300 15. Since order matters this is a permuation. nPr = n!/(n-r)! Since there are 25 members and we want to select 3 officers, we have 25P3 = 25!/(25-3)! = 25*24*23*22!÷(22!) = 25*24*23 = 13800 16. S = {1, 2, 3, 4, 5, 6, 7, 8, 9} 17. Since there are 10 digits a and 26 letters to choose from, we have 10*10*26*26*26*26*26 = 1,188,137,600 18. The complementary rule defines the P(A') as 1 - P(A), so 1 - 0.65 = 0.35. 19. P(woman) = 17/32 = 0.531 20. Since 7! = 7*6*5*4*3*2*1 and 5! = 5*4*3*2*1, 7! / 5! = 7*6*5*4*3*2*1 / 5*4*3*2*1 = 7*6 = 42 21. X = {0, 1, 2} P(X = 0) = .49 P(X = 1) = .42 P(X = 2) = .09 E(X) = n*p = 2*.3 = .6 V(X) = n*p*q, q = 1 - p = 1 - .3 = .7 V(X) = 2*.3*.7 = .42 standard deviation = sqrt(variance) = sqrt(.42) = .65 22. No. The sum of the probabilities is NOT equal to 1.
- 6. 23. 190/300. Simple probability is the result of the frequency of an event divided by the sample space. There are 190 transfer students in our sample of 300 students. 190/300 = 19/30 = .633... 24. Poisson

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