STAT200 QUIZ-2 1. Poll was conducted about two new movies, let's call them movie M1 and movie M2. 200 people were asked if they saw these movies. 100 people said they saw movie M1 (group 1), 70 people said they saw movie M2 (group 2), 20 people said they saw both movie, M1 and M2 (this number included in both groups). a) Draw a Venn diagram and identify number of people in each area. b) What is the probability that randomly selected person from this poll saw movie M1 or saw movie M2? P(M1 or M2) 2. There are 5 chips in the box. The chips are numbered 1 through 5: 1, 2, 3, 4, 5. You randomly take one chip from the box, record the number and put the chip back to the box. Then you take another chip from the box, record the number and put the chip back to the box. Then repeat it one more times with third chip. a) How many elements are in the sample space of this experiment? Use the Fundamental Counting Rule to find number of possible outcomes. 5x5x5=125 b) What is the probability that all three chips will have different number? Divide number of outcomes with all different numbers over total number of possible outcomes. 15/125 = 0.12 c) What is the probability that all three chips will have even numbers? Divide number of outcomes with all even numbers over total number of possible outcomes. 6/125 = 0.048 3. Table below shows Discrete Probability Distribution of Random Variable. Use these data to calculate Expected Value of x and Standard Deviation. x 10 12 14 16 18 P(x) 0.1 0.4 0.3 0.1 0.1 X p(x) x*p(x) x*x*p(x) 10 0.1 1 10 12 0.4 4.8 57.6 14 0.3 4.2 58.8 16 0.1 1.6 25.6 18 0.1 1.8 32.4 Exp val of x = 13.4 184.4 Standard deviation of x= 4.84 4. In how many ways can you select 3 people out of 8 candidates? Order of selection doesn't matter - use combinations. 8 7 1 6 2 336 = =56 3 6 I can select candidates in 56 ways. 5. There are 6 teams in a group. In how many ways can be one team on the first place, another team on the second and other team on the third? Order of teams makes a difference (what team on the first place, what team on the second and third). So, use formula for Permutation. 6*5*4=120 The teams can be in 120 different ways. 6. For this problem you should use Binomial Distribution Table given in Appendix. A fair coin tossed 8 times. Find the probability of getting a) Exactly 4 Heads. b) Less than 4 Heads (4 is not included). 7. Current unemployment rate of young college graduates is about 10% (probability 0.10). Find the probability that in 12 randomly selected young college graduates 2 will be unemployed. (Use Binomial Distribution Table given in Appendix). 8. Find the area under the standard normal distribution curve a) to the left of z = 0.44 b) to the right of z = 1.52 (use Appendix Table for Normal distribution). 9. Test score has Normal Distribution with a mean = 180 and a standard deviation = 10. Find probability that randomly picked score will be between 165 and 195? (Convert given data to z1, z2 and use Appendix Table for Normal Distribution) 10. Population data have Normal Distribution with mean = 80 and a standard deviation = 24. Multiple samples, each size of 100, were taken from population and Normal Distribution of Samples Mean was created. a) How mean and standard deviation in this Distribution of Sample Mean is different from Population Normal Distribution? b) Find the probability that sample mean will be less than 86. (see Chapter 9 in Lane e-book or Chapter 7 in Illowsky e-book). 11. Conducted survey of randomly selected 64 people (sample) shown that the time needed to complete one person's tax forms is 23.4 hours (the sample mean) hours. Assuming that population distribution is normal with a known standard deviation of 6.0 hours, construct a 90% confidence interval for the population mean time to complete the tax forms. (In formula for Margin of Error use z-value from Appendix Table for Normal Distribution) 12. Study conducted with 16 children (sample size), tried to evaluate how long it takes to learn to ride two-wheel bikes. It was revealed that it takes them an average of 4 months (sample average) with a sample standard deviation of 2 months.. Construct a 90% confidence interval for the population mean length of time needed to learn how to ride two-wheel bikes. (Population standard deviation is not known. For Margin of Error use t-value from attached Appendix Table for t-Distribution) Appendix Tables for Binomial, Normal and t-Distributions attached on a separate file