MATH220
Assignment #6
Question 1: The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.
a) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
b) Find the probability that if 50 randomly selected adults take the test, the mean time it takes the group to complete the test is less than 43 minutes.
c) Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
d) Does it seem reasonable that the mean of the 50 adults could be less than 43 minutes? Explain.
Question 2: Solve problem.
Question 3: A study by a federal agency concludes that polygraph tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive. A firm asks 12 job applicants about thefts from previous employers, using a polygraph to assess their truthfulness. Suppose that all 12 answer truthfully. Let X be the number of applicants who are classified deceptive.
a) Describe the probability mass function of X.
b) What is the probability that the polygraph says at least 1 is deceptive?
c) What is the mean number among 12 truthful persons who will be classified as deceptive? What is the standard deviation of this number?
d) What is the probability that the number classified deceptive is less than the mean?
Question 4: Solve problem.
Table C Attached
Question 5: A major manufacturing firm producing PCB for electrical insulation discharges small amounts from the plant. We assume that the amount of PCB discharge per water specimen is normally distributed with known standard deviation . Production will be halted if there is evidence that the mean PCB amount discharged in the water exceeds 3 ppm (parts per million). A random sample of 16 water specimens produced ppm.
a) Do these statistics provide sufficient evidence to halt the process? Use .
b) Briefly discuss the consequences of type I and type II errors. From your point of view, which of the two errors is the most serious?
c) Construct a 99% confidence interval for the true mean PCB amount discharged in the water.