The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for “slightly higher pay.” a. What is the probability that nine or more say yes? b. What is the probability that three, four, five, or six say yes? c. If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates? d. If 13 companies are contacted, what is the probability that all of the companies say there is a shortage of qualified job candidates? e. If 13 companies are contacted, what is the expected number of companies that would say there is a shortage of qualified job candidates?
ASSIGNMENT Problem 01: The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for “slightly higher pay.” a. What is the probability that nine or more say yes? b. What is the probability that three, four, five, or six say yes? c. If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates? d. If 13 companies are contacted, what is the probability that all of the companies say there is a shortage of qualified job candidates? e. If 13 companies are contacted, what is the expected number of companies that would say there is a shortage of qualified job candidates? Problem 02: According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per three-week period is Poisson distributed. a. What is the probability that the standard is not exceeded on any day during a three-week period? b. What is the probability that the standard is exceeded exactly six days of a three-week period? c. What is the probability that the standard is exceeded 15 or more days during a three-week period? If this outcome actually occurred, what might you conclude? Problem 03: A Department of Transportation survey showed that 60% of U.S. residents over 65 years of age oppose use of cell phones in flight even if there were no issues with the phones interfering with aircraft communications systems. If this information is correct and if a researcher randomly selects 25 U.S. residents who are over 65 years of age, a. What is the probability that exactly 12 oppose the use of cell phones in flight? b. What is the probability that more than 17 oppose the use of cell phones in flight? c. What is the probability that less than eight oppose the use of cell phones in flight? If the researcher actually got less than eight, what might she conclude about the Department of Transportation survey? Problem 04: A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of 1.2 hours per week shopping online. Assume that hours per week shopping online are Poisson distributed. If this survey result is true for all women and if a woman is randomly selected, a. What is the probability that she did not shop at all online over a one-week period? b. What is the probability that a woman would shop three or more hours online during a one- week period? c. What is the probability that a woman would shop fewer than five hours in a three-week period? Problem 05: An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River. Suppose six of the office workers are randomly selected. a. What is the probability that all six workers commute from the west side of the Rio Grande? b. What is the probability that none of the workers commute from the west side of the Rio Grande? c. Which probability from parts (a) and (b) was greatest? Why do you think this is? d. What is the probability that half of the workers do not commute from the west side of the Rio Grande? GOOD LUCK