Math 10 Prac Exam 2 Name Use the following information to answer questions 1-3. A horse racer wagers on thoroughbred horses. He only bets for a horse to win first place. Over time, it has been established that the chance of wining a given race is .15. 1. The racer is interested in the number of bets he makes until he gets his first win. Write the expression that represents that chance he will bet 39 times. 2. Out of 22 races, how many races does the bettor expect to lose? Show your calculation not just your final number. Hint: Is this the same distr. as in (1)? Use the correct symbol. 3. A school raises money with a raffle selling each ticket for 3$. There are 230 tickets and you purchase 8 tickets. Use this information to decide if the game is fair by setting up the RV and a PDF first. Show your calculation for the expected value of the game. The prize is worth 500$ X= PDF Is this a fair game? Yes or can be used to make it fair. no If not circle one strategy below that ______________________________________________________________________________ ________4. Suppose the amount of ice cream sold during the summer weekends is uniformally distributed between 5 and 24gallons Write the distribution with parameter values. a) Draw the pdf labeling everything as shown in class. b) Find the chance the ice cream sold on a summer weekend will be between 17-21 gallons. Shade in the corresponding region in (a). c) Find the amount representing the 14 th percentile. Include a new picture! 5. To estimate the mean cost of material/course a department samples 96 students and gets an average cost of $60.50 with a standard deviation of $22. Use this information to construct a 92% confidence interval. Include the picture with as much detail as shown in class. The age of a car in a particular city is normally distributed with a mean of 12.8 years and a standard deviation of 2.4 years. Use this information to answer questions below. You must include a picture with the same detail as shown in class. When samples are drawn n=28 6. Find the probability that a car is more than 10 years old. 7. Find the chance that the mean age of 28 cars is less than 12 years. 8. Find the chance that the mean age is 12.8 years. 9. Find the mean age representing the 98th percentile. ______________________________________________________________________________ ________ 10. Suppose each family is asked how much they spend on their kid's school supplies. If there are 180 families and they are interested in the average amount spent based on 36 families then the sample size is five. a) true b) false 11. X=duration of a play and normally distributed with a mean of 95 minutes. X =sample mean duration . First circle which is less likely a or b. explain why and. Include a pic as shown in class.. a) P(X < 50) or b) P( X < 50) 12. Given the confidence interval (13.56, 16) find the following (show some work!) a) What was the point estimate? b) What was the EB? _ ______________________________________________________________________________ ___ 13. If all other values remain constant in the construction of a confidence interval and only the sample size decreases, the interval length will also decrease. Show your reasoning by writing out the EB a) true b) false 14. A company wants to find the minimum sample size needed to estimate the average lifespan of a part within 3 months with a 90% confidence level. If the population standard deviations is known to be 13.8 months, what sample size should they use to estimate the true mean lifespan? Include a picture with 1 axis. 15. Over half of professional educators feel learning material should be low cost or free. Suppose out of 160 educators 98 agreed. Create a 90% confidence interval. Include a pic with the same level of detail as shown in class.. 16. Suppose we are interested in the percent of Cali voters that will vote in the next election. If we want the sample size with 99% confidence, how many voters must we sample? 17. In one sentence what does the CLT allow us to do