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 120 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.)
Right!
0.0569
To determine the task times that qualify individuals for advanced training, we need to find the corresponding z-score that represents the fastest 10% of the distribution.
Step 1: Convert the percentiles to z-scores.
Since we want to find the fastest 10% of the distribution, we are looking for the z-score that corresponds to the upper 10% (or the lower 90%) of the distribution.
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the lower 90% is approximately 1.28.
Step 2: Use the z-score formula to find the corresponding task time.
The z-score formula is given by:
z = (x - μ) / σ
where:
z = z-score
x = task time
μ = mean value of the distribution
σ = standard deviation of the distribution
Rearranging the formula, we have:
x = z * σ + μ
Substituting the known values:
x = 1.28 * 25 + 120
Calculating the task time:
x = 32 + 120
x = 152 seconds
Therefore, individuals who complete the task in approximately 152 seconds or less qualify for advanced training.