uiz - 2 1. What is the probability of rolling a pair of dice and a) obtaining a total score of 8? b) obtaining a total score of 11 or more? 2. A pack of M&M candies contains 20 red, 15 blue and 5 yellow candies. Two candies were randomly taken from the pack without replacement (taken candy was not returned to the pack). Find the probability that a) both candies are red; b) the first candy is yellow and the second candy is blue. Tip: use formula for P(A and B) 3. In the shown Venn Diagram N(total) = 200 is total number of students N(A) = 70 students take Statistics N(B) = 60 students take Calculus N(AB) = 30 students take both courses, Statistics and Calculus. N Based on the given data find the probability that student a) takes Statistics, but do not take Calculus. b) do not take Statistics or Calculus (remember, probability cannot be greater than 1). A B 4. A fair coin is flipped 8 times. What is the probability of getting exactly 5 heads? Use formula or Table for Binomial distribution. 5. In a spinning wheel casino game you pay $5 and can win $1, $5, $10, $20 or lose your bet. A random selected guest played 20 times. Data below shows how many times each option was happened. Lose - 6 times $1 win - 7 times $5 win - 4 times $10 win - 2 times $20 win - 1 times Complete table for Discrete Probability Distribution in this case and calculate expected value E(x). X, $ you get from each game 0 1 5 10 20 P(x) E(x) = 6. Calculate a) Permutations P(6,3). b) Combinations C(6,3) 7. According to statistics, about 30% of adult American do not have credit cards. If randomly 12 adult Americans were selected, what is the probability that less than 4 will not have credit cards? Use the Appendix Table for Binomial distribution 8. Use the Appendix Table for Normal distribution and find the area under the standard normal distribution curve a) to the left of z = 0.35 b) to the right of z = 1.84 9. Assuming an average life expectancy has Normal Distribution with a mean = 77 and the standard deviation = 10, find the probability that a person life expectancy will be between 70 and 80? (Tip: convert 70 and 80 to z1, z2 and use the Appendix Table for Normal Distribution to find probability that z will be between z1 and z2). 10. Measurements were taken N=10 times (sample size). It was found that sample average is x =18.3 with a sample standard deviation of s=0.5. Construct a 90% confidence interval for the population mean. (Population standard deviation is not known. For Margin of Error use t-value from attached Appendix Table for t-Distribution)