Question

A survey showed that the probability that an employee gets placed in a job that is suitable for the employee is 0.65. A psychometric test consultant claimed that he could help place any employee in a suitable job based on the result of a psychometric test. An employee working in a particular company decides to take this test. The test has an accuracy rate of 70 1) True 2) False

Answer 1

The given statement is indeterminate without the probability of the test being positive when the employee is not in a suitable job. Therefore, it cannot be definitively classified as true or false based on the given information"is False.

Step-by-step explanation:

The probability of an employee getting placed in a suitable job is given as 0.65. The psychometric test consultant claims an accuracy rate of 70%. Let's denote the event of an employee being placed in a suitable job as A and the event of the psychometric test indicating suitability as B. The consultant's claim translates to P(B|A) = 0.70, the probability of the test being positive given the employee is in a suitable job. The probability of an employee being in a suitable job is P(A) = 0.65.The given statement is False.

To find the overall probability of the test being accurate (A and B both happening or both not happening), we use the formula for conditional probability: P(A and B) = P(B|A) * P(A). Substituting the given values, we get P(A and B) = 0.70 * 0.65 = 0.455. Now, we need to consider the probability of the test being positive when the employee is not in a suitable job, denoted as P(B|¬A). The complement of A (¬A) is the event of the employee not being in a suitable job, and the problem does not provide this probability.

Without this crucial information, we cannot accurately calculate the overall probability of the test being accurate. Therefore, the claim made by the psychometric test consultant cannot be determined to be true based on the information given. The answer is False due to the lack of data on P(B|¬A).