Question

The plant manager of a manufacturing facility is concerned about drug use among plant workers and plans to implement random drug testing. One of the tests to be applied measures the level of factor-X in blood samples. Among recent users of cocaine, the level of factor-X is normally distributed with a mean of 10.0 and a standard deviation of 1.3. Among non-users, the level is normally distributed with a mean of 6.75 and a standard deviation of 1.5. The employer plans to send a warning letter to all employees with a factor-X level of x or greater, with x to be determined. 1

(a) Find the value of x that will ensure that 90% of recent cocaine users will be sent a warning letter. (b) If your answer to part

(a) is adopted, what proportion of non-users will also be sent warning letters?

Answer 1

(a)

Here we have

Here we need z-score that has 0.90 area to its right. The z-score -1.28 has 0.90 area to its right. The required X is

Answer: 8.336

(b)

Here we have

Here we need z-score for X = 8.336 so

The  proportion of non-users will also be sent warning letters is

Answer: 0.1453