Question 779620: (a) Two identical urns, Urn I and Urn II are on a table. Urn I contains one red and one black marble. Urn II contains two red marbles. An Urn is selected at random and then marble is randomly drawn from it. The marble is red. Find the probability that the marble came from Urn II, given that the marble is red.
(b) Almost all companies utilize some type of year-end performance review for their employees. Human Resource [HR] at the University of AP Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, “if you have this tendency, consider using a normal distribution 5% of employees (rated) exemplary, 25% distinguished, 50% competent, 15% marginal and 5% unacceptable.” Suppose that rating an employee’s performance is any real number on a scale from 0(lowest) to 100(highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 15.
(i) What is the lowest rating you should give to a “competent” employee if you follow the University of AP HR guidelines?
[5 marks]
(ii) What is the lowest rating you should give to an “exemplary” employee if you follow the University of AP HR guidelines?
(c) Given that the height of college students is normally distributed with mean 62 inch and standard deviation is 4 inch and that the minimum height required joining a police academy is 64 inch. Find the percentage of students who would be rejected on account of their height.
(d) The pass rate of first-takers for the bar examination at a certain jurisdiction is 72%. Of those who fail, 88% pass their second attempt. Find the probability that a randomly selected law school graduate becomes a lawyer. [Candidates cannot take the examination more than twice]
Answer by psbhowmick(878)   (Show Source):
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