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MATH 2311 Final Exam Review The probability that a randomly selected person is left handed (the event L) is P(L) = 0.1 and the probability that a randomly selected person is a blonde (the event B) is P(B) = 0.3. The probability that a randomly selected person is left handed and a blonde is 0.02. Find the probability that a randomly selected person either is left handed, a blonde, or both. Among 9 lightbulbs produced exactly two is known not to function properly. If 3 lightbulbs are selected randomly, find the probability that exactly one does not function properly. Given the following sampling distribution: What is P(X < 3)? Given the following sampling distribution: Determine the mean of the distribution. Given the following sampling distribution: Determine the variance of the distribution. Suppose you have a distribution, X, with mean = 75 and standard deviation = 8. Define a new random variable Y = 2X - 15. Find the mean and standard deviation of Y. In testing a study technique, researchers found that 15% of all students using it will have increased scores. A random sample of 25 students using the technique is selected. Find the probability that exactly three will have increased scores. A manufacturer of paperclips randomly and independently puts 200 paperclips in each box produced. The company knows that 1 percent of the clips will break. What is the probability that a box will have one or fewer paperclips break? Each year a high school selects a number of students for a summer camp program. On average, 60 percent of those selected attend the program. Out of the 35 students selected, what is the probability that exactly 15 attend the program? A batter has an RBI of 0.16. We want to observe this batter during one game to see how many atbats he has before his first home run. What is the probability that the batter’s first homerun is on his third time to the plate? The length of time needed to drive to school is normally distributed with mean 32 minutes and standard deviation 7 minutes. Find the probability that it will take less than 27 minutes to drive to school. Find a value of c so that P(Z > c) = 0.23. A random sample of 1000 soda cans is pulled from an assembly line. Prior experience has shown that the distribution of the contents has a mean of 8 ounces and a standard deviation of 0.09 ounce. What is the probability that the mean contents of the 1000 sample cans is less than 7.5 ounces? In a large population, 72% of the households have multiple cars. A simple random sample of 150 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions? In a large population, 72% of the households have multiple cars. A simple random sample of 150 households is to be contacted and the sample proportion computed. What is the probability that the sample distribution has a proportion less than 70%? Determine the correlation coefficient of the following data: Determine the LSRL of the data: Determine the residual of the data for the value of x = 6. Based on the tw0-way distribution table, what percent of married people drive vans? A simple random sample of 100 kindergarteners indicated that 71% of them have imaginary friends. Find the 95% confidence interval that estimates the proportion of them that have imaginary friends. A test has been done to show the effectiveness of a new drug. The treatment group, 45 people, had 25% improvement rate, and the placebo group, 35 people, had a 10% improvement rate. Determine the 90% confidence interval for the difference in improvement rates. The height of 8th graders is known to have a standard deviation of 4 inches. A simple random sample of 81 of them is chosen and found to have a mean height of 52 inches. Construct a 89% confidence interval for the mean height of 8th grade students. A study is conducted to determine the mean height of college students. A group of 50 men had a mean height of 70 inches with a standard deviation of 4 inches. A group of 40 women had a mean height of 66 inches with a standard deviation of 5 inches. Determine the 95% confidence interval for the difference in mean heights. A company wants to determine the proportion of people in Houston that have premium cable service. How many people must be surveyed to have a confidence level of 98% with a margin of error of 3%? A coin is flipped 200 times and landed on heads a total of 135 times. Test the two-sided claim, with confidence of 5%, that the coin is fair. A gym wanted to determine if more men or women took fitness classes. Out of 55 men surveyed, 25 took fitness classes, and out of 75 women surveyed 45 of them took fitness classes. Is the difference in proportions statistically significant, with significance level of 5%? A automated card-dealer is tested to show if it is favoring one suit of cards. Out of 100 cards dealt, there were 35 clubs, 15 spades, 20 hearts, and 30 diamonds. Test using a chi-squared process to determine if the machine is dealing fairly, using significance of 1%. There is a claim that African-Americans are more susceptible to heart disease. A study is conducted where 50 African-Americans are tested, showing that 15 have some form of heart disease, and 40 non-African-Americans were tested to show that 9 have some form of heart disease. Test this claim, with a significance level of 5%.