Elementаry Prоb. аnd Stаts – Test 2 Cоnsider the fоllowing data: Condition Present Condition Absent Test Result + 150 10 Test Result - 25 70 One person is randomly selected from the group (a) Find Prob( Test Result - ) (b) Find Prob( Test Result + and Condition Absent ) For the data in question 1, find: (a) Prob( Condition Present | Test Result - ) (b) Prob( Test Result + | Condition Absent ) If P(A)=0.65, P(B)=0.1 and P(A or B)=0.3, find P(A and B). Are the events in question 3 mutually exclusive ? Explain. Laura has 7 Stats textbooks that she is going to place on a shelf. How many different arrangements of the books are possible if the order of the books on the shelf matters to Laura. A university advertises to fill 2 positions for Statistics teachers. 23 people apply. In how many ways can the positions be filled ? (a) Calculate 7P3 (b) Calculate 14C0 X 0 1 2 3 P(X) 0.7 0.05 ? 0.1 What does P(2) equal for this to be a probability distribution? What is the expected value of the probability distribution in question 8. a) For a binomial experiment, how many outcomes are possible for each trial ? b) In a binomial experiment, is it possible for the probability of success to change from one trial to the next ? Consider a binomial experiment with n=10 trials where the probability of success on a single trial is p=0.7. Find Prob(r=4). (a) What is the expected value of the binomial distribution in question 11 ? (b) What is the standard deviation of the binomial distribution in question 11 ? An unfair coin has prob(heads)=0.4. The coin is tossed. What is the prob. that the first tail occurs on the 7th toss ? A gale force wind occurs on average once every 60 hours on a mountain road. For an interval of 300 hours, what is the prob. that 3 gale force winds are experienced ? Hint, use a Poisson distribution. Allison is a 65% basketball free throw shooter. She is interested in how many attempts it takes to make 4 baskets. What is the probability that it takes 12 attempts ? What is the mean and standard deviation of the Standard Normal distribution ? What does the empirical rule say about the approximate percent of observations in a normal distribution that lie within 2 standard deviations of the mean? Assume that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches. Using the empirical rule, what is the approximate percentage of college women who are shorter than 67.5 inches. What does a z-score represent ? Consider a normal distribution with mean=20 and standard deviation=4 (a) Find a z value corresponding to an x value of 14 (b) Find the data value corresponding to a z value of 1.5 Find the area under the standard normal curve (a) To the right of z=1.52 (b) Between z=1.40 and z=2.03 If x has a normal distribution with mean=40 and standard deviation=15, find Prob ( 30
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