1) According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse. (Hint: Does this satisfy the assumptions of a Binomial experiment? Use the Complerment Rule to find the probability.)
2) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.
3) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,610 with a standard deviation of $700. What is the 95% confidence interval for the true mean resale value of a 5- year-old car of this model? 1
4) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is about 5% ?
5) A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows:
6) A) 67% B) 78% C) 98% D) 233% Solve the problem.
7) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will occur next month on this stretch of road. 2 MULTIPLE CHOICE. Select the correct answer from the choices provided.
8) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 41% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?
8) A) Yes, the sample is a random and independent sample.
B) Yes, the sample size is n = 20.
C) No, a binomial distribution requires only two possible outcomes for each experimental unit sampled. D) No, the employees would not be considered independent in the present sample.
9) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below:
(Hint: Which rule of probability governs the OR of two events?)
10) In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events "red or black" and "missing cap" dependent or independent? Explain.