Question

Question: The time it takes an employee to package the components of a certain product is normally distributed with = 8.5 and = 2.5 minutes. As an incentive, management has decided to give a bonus to the 25% of employees who took the shortest amount of time to package the components. Find the amount of time taken to package the components that will indicate that

The time it takes an employee to package the components of a certain product is normally distributed with = 8.5 and = 2.5 minutes. As an incentive, management has decided to give a bonus to the 25% of employees who took the shortest amount of time to package the components. Find the amount of time taken to package the components that will indicate that an employee should get a bonus. (Round your answer to two decimal places.)

An employee must package components in a time ---Select--- (more than less than) _____ minutes.

Answer 1

To find the time that an employee must package the components to receive a bonus, calculate the first quartile (Q1) of the normal distribution for the given mean (8.5) and standard deviation (2.5). The corresponding time, after rounding, is less than 6.82 minutes.

Step-by-step explanation:

The student needs to find the maximum time taken to package components that will indicate an employee is in the fastest 25%. Since the times are normally distributed, we need to find the first quartile (Q1) of the normal distribution. Given the mean (μ) is 8.5 minutes, and the standard deviation (σ) is 2.5 minutes, we will use the z-score table to find the z-score that corresponds to the cumulative probability of 0.25 (25%).

Using a standard normal distribution table or a calculator, we find that the z-score for 0.25 is approximately -0.674. We then use the formula X = μ + (z * σ) to convert the z-score to the actual time. Substituting the given values:

X = 8.5 + (-0.674 * 2.5) = 8.5 - 1.685 = 6.815 minutes.

After rounding to two decimal places, an employee must package the components in less than 6.82 minutes to receive a bonus.