<p>Math 227 Winter 2014 Practice Final</p><p>#1 True/False ______(a) The standard deviation, s, is not effected by extreme data.</p><p>______(b) If the population distribution is not normally distributed, the distribution for the sampling mean will be approximately normally distributed for n = 20.</p><p>______(c) 5/3 cannot be an answer for a probability.</p><p>______(d) On a five possible answers multiple-choice question, the probability of answering the question correctly by random guessing is 1/2.</p><p>______(e) With the same level of confidence and the same standard deviation, as n increases the width of the confidence interval increases.</p><p>______(f) The claim is always the same as Ho.</p><p>#2 A card is selected randomly from a deck of cards, what is the probability that a face card (Jack, Queen, King) or a club will be selected.</p><p>#3 Two dice are tossed. What is the probability of getting a sum of 8?</p><p>#4 A carton contains 12 eggs, 3 of which are cracked. If we randomly select 2 eggs, one after the other without replacement, what is the probability that both of the cracked eggs are selected? #5 Listed below are the Titanic mortality data. Men Women Boys Girls</p><p>Survived 332 318 29 27</p><p>Died 1360 104 35 18</p><p>(a) If we randomly select someone who was aboard the Titanic, what is the probability of getting a man or a person who survived?</p><p>(b) What is the probability of getting a woman, given the selected person died?</p><p>#6 (a) Find P(x = 3) for the following probability distribution table.</p><p> x 1 2 3 4 P(x) 0.12 0.21 ? 0.18</p><p>(b) Find the mean of the probability distribution.</p><p>#7 It was found that 55% of American victims of health care fraud are senior citizens. If 20 victims are randomly selected, (a) find the probability that exactly 14 are senior citizens.</p><p>(b) find  and  for this binomial distribution. #8 The average amount of rain per year in Greenville is 49 inches. The standard deviation is 8 inches. Find the probability that next year Greenville will receive the amount of rainfall in between 46 and 54 inches.</p><p>#9 If the average score of a reading test is 122.6 with the standard deviation of 18, find the cutoff-score for the bottom 5%. Assume the variable is normally distributed.</p><p>#10 The average annual salary in Pennsylvania was $24,393 in 1992. Assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $4362. Find the probability that, for a randomly selected sample of 25 individuals, the mean salary was less than $26,000. #11 A researcher is interested in estimating the average monthly salary of sports reporters in a large city. He wants to be 99% confident that his estimate is correct. If  = $1100, how large a sample must be selected if he wishes to be accurate to within $150?</p><p>#12 A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.</p><p>#13 An attorney claims that more than 25% of all lawyers advertise. A sample of 200 lawyers in a certain city showed that 63 had used some form of advertising. At  = 0.05, is there enough evidence to support the attorney’s claim? #14 A state executive claims that the average number of acres in western Pennsylvania state parks is less than 2000 acres. A random sample of five parks is selected, and the number of acres is shown.</p><p>959 1187 493 6249 541</p><p>(a) Use your calculator to find the sample mean and the sample standard deviation.</p><p>(b) At  = 0.01, is there enough evidence to support the claim?</p><p>#15 Heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men between 155 cm and 197 cm?</p><p>#16 Jim gets test grades of 79, 75, 82, and 85. He gets a 94 on his final exam. Find the weighted mean if the tests each count for 10% and the final exam counts for 60% the final grade.</p><p>#17 If Z is a standard normal variable, find the probability that Z is greater than -2.89.</p><p>#18 Determine whether the given procedure results in a binomial distribution. Why or why not? Toss a coin 25 times, keeping track of the number of tails. #19 There are 9 members on the board of directors for a hospital. If they must elect a chairperson, vice chairperson, and a secretary, how many different slates of candidates are possible?</p><p>#20 For the following data: 14 15 8 11 8 8 9 1 12 8 7 15</p><p>(a) Find the Mea</p><p>(b) Find the Median</p><p>(c) Find the Mode</p><p>(d) Find the Five-number summary (Low, Q1, Q2, Q3, High)</p><p>(e) Construct a boxplot</p><p>#21 Find the z value to the left of the mean so that 60.64% of the area under the distribution curve lies to the right of it.</p><p>#22 Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find the probability that the student makes between $13,000 and $14000.</p><p>#23 Given the equation of the regression line y' =6.00 + 4.00 x and the correlation coefficient r = 0.987 , find the best predicted value of y for x = 2.00. What is r? #24 State the Central Limit Theorem or four requirements for a Binomial Experiment.</p><p>#25 Find the p-value for a right tailed test with observed z = 2.16</p><p>#26 One survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke. Use a = 0.05 to test the claim that the percentage (p) of smoking among those with four years of college is less than the 27% rate for the general population.</p><p>#27 The mean is m =125.0 and the standard deviation is s = 5.0 , find the probability that X is between 135.0 an d143.2. X has a normal distribution</p>