According to a manager it takes an average weekday commute of 39 minutes with a Standard Deviation of 7 minutes for the employees to get to work when they use their personal vehicles for their office commute while management set a policy of not more than 40 minutes for their daily one-way commute. A survey conducted one day on 70 employees showed an average of 34 minutes commuting time using the metro public transportation system with a Standard Deviation of 21 minutes. For the employees choosing to increase their chances to come on time using personal transportation their variation should be reduced to ___________?

Question

According to a manager it takes an average weekday commute of 39 minutes with a Standard Deviation of 7 minutes for the employees to get to work when they use their personal vehicles for their office commute while management set a policy of not more than 40 minutes for their daily one-way commute.  A survey conducted one day on 70 employees showed an average of 34 minutes commuting time using the metro public transportation system with a Standard Deviation of 21 minutes. For the employees choosing to increase their chances to come on time using personal transportation their variation should be reduced to ___________?

Quizplus · Accepted Answer

The goal is to reduce the variation in commute time for employees who use personal transportation. To do this, we want to decrease the standard deviation of the commute times. We can use the formula: New Standard Deviation = Old Standard Deviation / Square Root of Sample Size.

For personal transportation, the new standard deviation would be 7 / Square Root of 70, which is approximately 0.84. To reduce the variation to be within the management's policy of not more than 40 minutes for their daily one-way commute, we need the new standard deviation to be less than or equal to 1. Therefore, we need the new standard deviation to be reduced by 6.16 (40 - 39 - 0.84).

Therefore, the new standard deviation for personal transportation should be approximately 6.16 minutes less than the old standard deviation of 7 minutes, which is approximately 0.84 x 6.16 = 5.18. Thus, the variation should be reduced by 5.18, which is approximately 3.5 minutes (since the commute times are in whole minutes).

Therefore, the best choice is C.

According to a Manager It Takes an Average Weekday Commute