15.Math-Review. Review 2. Exercises.
(a) What is the expected annual compensation for a new hire?
(b) What is the standard deviation of the annual compensation for a new hire?
(c) What is the expected annual compensation after completing a year in the firm, I.e., just after the salary increase is announced?
(d) What is the probability that the annual compensation after completing a year in the firm, i.e., just after the salary increase is announced, will exceed $140,000?
(Hint: The annual compensation is also normally distributed).
(a) What is the probability that all 10 microchips in the sample are not defective?
(b) What is the probability that the inspector accepts the first microchip?
(c) What is the probability that the inspector accepts 9 (out of 10) microchips?
(d) Given that the inspector accepts a microchip, what is the probability that it has no defect?
(a) Determine the probability that the witnesses give conflicting testimony.
(b) Which witness is more likely to commit perjury?
(c) What is the conditional probability that Al is innocent, given that Bo and Ci gave conflicting testimony?
(d) Are the events “Bo tells a lie” and “Ci tells a lie” independent? Are these events conditionally independent to an observer who knows whether or not Al is guilty?
Does this distribution sum to 1?
(a) None of the four bulbs fails during its first month of use.
(b) Exactly two bulbs have failed by the end of the third month.
(c) Exactly one bulb fails during each of the first three months.
(d) Exactly one bulb has failed by the end of the second month, and exactly two bulbs are still working at the start of the fifth month.
(b) Bo is more likely. 0.16 > 0.06.
(d) First question NO. Second YES.
(b) 80.89% of Snowboard Inc.
(b) P(X<50) = 0.18805
(c) P(45<=X<=55) = 0.86775