Question

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

Answer 1

To qualify for advanced training, individuals should have a task time less than or equal to 113.8 seconds.

Step-by-step explanation:

To find the task times that qualify individuals for advanced training, we need to find the value that corresponds to the fastest 10% of task times. Since the task time is normally distributed, we can use the z-score formula to find this value.

First, we convert the desired percentile to a z-score using the standard normal distribution table. The z-score corresponding to the 10th percentile is approximately -1.28.

Next, we use the formula z = (x - mean) / standard deviation and solve for x to find the task time that corresponds to the z-score. Substituting the values, we get -1.28 = (x - 145) / 25. Solving for x, we find x ≈ 113.8.

Therefore, individuals with a task time less than or equal to 113.8 seconds qualify for advanced training.