1) For a random sample of twenty five students from a large class, the accompanying table shows the amount of time spent studying for a test. Study time (hours) 0-4 4-8 8-12 12-16 16-20 Number of students 3 7 8 5 2 a) Estimate the sample mean study time b) Estimate sample standard deviation 0) In which class is the sample median? (1) Which is the modal class? 2) A sample of 10 students in your class record the time they spent studying (in minutes), & then later looked at their grades to obtain the following data: Time spent studying (X) 40 42 47 47 25 44 41 48 35 28 Grades (Y) 78 63 80 85 50 79 84 92 94 48 a) Calculate the covariance and correlation (Note: use sample covariance formula) b) Interpret your results 3) Number of games Frequency 1 5 2 6 - lO 7 ll - 15 8 l6 - 20 3 a) Estimate the mean number of games b) Find the modal interval 4) A corporation receives a particular part in shipments of 100. Research has indicated the probabilities shown in accompanying table for numbers of defective parts in a shipment. Number defective 0 1 2 3 more than 3 Probability .29 .36 .22 .10 .03 a) What is the probability there will be less than three defective parts in the shipment b) What is the probability there will be more than 1 defective part in a shipment c) The ve probabilities in the table sum upto one. Why must this be so? 5) Suppose that you have an intelligent friend who has not studied probability. How would you explain to your friend the distinction between mutually exclusive events and independent events 6) Which of these numbers cannot be a probability? a) -0.00001 b) 0.5 c) 1.001 d) 0 e) l f) 20% 7) Two coins are tossed; nd the probability that two heads are obtained. 8) A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random; what is the probability that this marble is white? 9) Three unbiased coins are tossed. What is the probability of getting at most two heads? 10) What is the probability of getting a sum 9 from two throws of a dice