Probability and Statistics Name______________________________ 3rd 9 Weeks Exam Review (WITH PROBABILITY): Day 1 Directions: 1. a. b. Directions: 2. Probability Distributions. Determine the missing probability. x P(x) 3 0.398 6 ? 9 0.166 12 0.410 x P(x) 1 1/17 2 5/17 3 3/17 4 ? Probability Distributions. Find the mean, variance, and standard deviation of the following. a. x P(x) 0 0.12 1 0.2 2 0.31 3 0.25 4 0.12 Mean = ______________ Variance = ____________ St. Dev = _____________ b. x P(x) 8 0.15 9 0.25 10 0.29 11 0.19 12 0.12 Mean = ______________ Variance = ____________ St. Dev = _____________ c. x P(x) 0 0.17 1 0.26 2 0.13 3 0.24 4 0.20 Mean = ______________ Variance = ____________ St. Dev = _____________ Directions: 3. Binomial Distributions. Answer the following. The probability that a woman will color her hair is 0.72. What is the probability that in a randomly selected group of 25 women, a. exactly 15 will color their hair? b. at least 20 will color their hair? c. 4. at most 10 will color their hair? The probability that a person has fallen asleep while talking on the phone is 0.34. What is the probability that in a randomly selected group of 20 people, a. exactly 7 have fallen asleep while talking on the phone? b. at least 13 have fallen asleep while talking on the phone? c. 5. at most 8 have fallen asleep while talking on the phone? Approximately 75% of students have tried driving without a license. What is the probability that in a randomly selected group of 40 people, a. exactly 30 students have driven without a license? b. at least 28 students have driven without a license? c. 6. at most 31 students have driven without a license? Approximately 72% of toddlers are willing to try peas. In a group of 45 toddlers, what is the a. mean number of toddlers willing to try peas? b. standard deviation? 7. Approximately 33% of teachers have more than one college degree. In a school with 120 teachers, what is the a. mean number of teachers who have more than one degree? b. the standard deviation? Directions: Standard Normal Distributions. Find the following. 8. What is the mean and standard deviation of a standard normal curve? 9. State the empirical rule. a. b. c. 10. Percentage within 1 standard deviation about the mean: __________ Percentage within 2 standard deviations about the mean: __________ Percentage within 3 standard deviations about the mean: __________ a. P(0 z 2.35) b. P(2.10 z 2.34) c. P ( z 0.13) d. P( z 1.48) Directions: Normal Applications. Find the following. 11. Pizza delivery time is normally distributed. Pizzas are delivered in 30 minutes on average with a standard deviation of 5.9 minutes. What is the probability it will take more than 40 minutes for your pizza to be delivered? 12. Assume that women’s heights are normally distributed with a mean of 64.5 inches and a standard deviation given by 2.2 inches. a. If a woman is randomly selected, find the probability that her height is less than 65 inches. b. What height would a woman be if she was in the top 10% of the population? 13. The average cholesterol content of a certain brand of eggs is 216 mg with a standard deviation of 15 mg. Assume the variable is normally distributed. If an egg is selected, find the probability that the cholesterol content will be between 210 mg and 220 mg. Directions: Find the following probabilities. 14. If the probability of NOT owning a cell phone is 0.12, what is the probability that a person does own a cell phone? 12. A card is drawn from a standard deck of cards. What is the probability it is a diamond? 13. A jar contains 3 red, 2 black, 6 purple, and 3 yellow balls. What is the probability of randomly drawing a purple ball? 14. Students were asked if they watched college football. The results are in the chart below. Watch College Does NOT watch Football college football 9th graders th 12 graders 32 84 73 43 If a student is selected at random, what is the probability that he or she will be a 9th grader or watch college football? 15. In a survey of high school students, 326 students said they have texted during class and 98 said they had not. From this, we can calculate the probability that a student will text during class. Is this a theoretical or experimental (empirical) probability? 16. The probability of getting 3 of a kind in poker is about 2.11%. Is this a theoretical or experimental (empirical) probability? 17. A group of high school students were asked if he or she had a video game system. The results are listed below. Owns a gaming system male female 258 157 Does NOT own a gaming system 81 103 If a student is selected at random, what is the probability that the student will own a video game system, given that the student is female? Directions: Answer the following. 18. Which measure determines the expected value of the variable? 19. Use the table to answer the following questions. x P(x) 1 0.27 2 0.34 3 0.16 4 0.09 5 x a. Find the missing value. b. Find the expected value. c. Find P ( x 4). d. Find Px 2. 20. A school group is selling $3 raffle tickets. The first prize is $4,500 and the second prize is $1,000. There are 10 prizes of $20 gift certificates. The number of tickets sold is 4500. You purchase 1 ticket. Find the expected value of the gain. 21. A cash prize of $3500 is to be awarded in a raffle. If 1800 tickets are sold at $5 each, find the expected value of the gain if you purchase 2 tickets.