1) Over the course of a year, the probability that a house in an urban area will be burglarized is 4%. a) If 20 houses are randomly selected, what is the probability that exactly 2 of the houses will be burglarized? b) If 20 houses are randomly selected, what is the probability that 2 or fewer of the houses will be burglarized? 2) Fiftyseven percent of families say that their children have an inuence on their vacation plans. Consider a sample of eight families who are asked if their children inuence their vacation plans. Is this a binomial experiment? If so, identify the values of n, p, and q, and list the possible values of the random variable x. 3) a) Find the mean and standard deviation of the binomial distribution for which n = 1000 and p = 0.94. b) List the possible values of the random variable x for the distribution. c) Which values of x would be usual to observe? 4) The probability that an individual is lehanded is 0.12. In a class of 39 students, what is the probability of nding 5 left- handers? 5) According to a police source, a car with a certain protection system will be recovered 89% of the time. Find the probability that 3 of 7 stolen cars will be recovered. 6) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear glasses? 7) a) State the mean and standard deviation of the standard normal curve. b) For the standard normal curve, nd the z-score that corresponds to the 20th percentile. c) Does this mean that 20% of z-scores are below or above the z-score that you found in part b? 8) a) State the mean and standard deviation of the standard normal curve. b) Find the z-score for which 90% of the distribution's area lies between 2 and z. 9) The length of similar components produced by a company is approximated by a normal distribution model with a mean of 5 cm and a standard deviation of 0.02 cm. If a component is chosen at random, a) what is the probability that the length of this component is between 4.98 and 5.02 cm? b) what is the probability that the length of this component is between 4.96 and 5.04 cm? 10) Given a distribution with u = 60 and o = 10, what random variable (x) corresponds to the 98th percentile? Conclude your post with: Only 2% of x values will be above 11) Given a distribution with p. = 60 and c = 10, find the z score that corresponds to x = 74. Is 74 a usual or unusual data value in this data set? 12) A large group of students took a test in Physics and the nal grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students, a) scored higher than 80? b) should pass the test (grades 2 60)? 0) should fail the test (grades