Due to excessive pollution, GREEN Solutions Inc. is considering subsidizing public transportation to work for its employees. According to the manager it takes an average weekday commute of 39 minutes with a Standard Deviation of 7 minutes for the employees to get to work while they use their personal vehicles for their office commute while the 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. Assuming a Normal Distribution for the commute times by either personal or public transportation, which of these is true?

Question

Due to excessive pollution, GREEN Solutions Inc. is considering subsidizing public transportation to work for its employees.  According to the manager it takes an average weekday commute of 39 minutes with a Standard Deviation of 7 minutes for the employees to get to work while they use their personal vehicles for their office commute while the 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. Assuming a Normal Distribution for the commute times by either personal or public transportation, which of these is true?

Quizplus · Accepted Answer

We need to compare the probability of arriving on time (within 40 minutes) using personal vehicles versus the MPTS. To do this, we need to standardize the commute times using the Z-score formula: Z = (X - μ)/σ, where X is the commute time, μ is the mean commute time, and σ is the standard deviation.

For personal vehicles: Z = (40 - 39)/7 = 0.14. From the Z-table, the probability of Z being less than or equal to 0.14 is 0.5557 or 55.57%, which is the probability of arriving on time using personal vehicles.

For MPTS: Z = (40 - 34)/21 = 0.29. From the Z-table, the probability of Z being less than or equal to 0.29 is 0.6151 or 61.51%, which is the probability of arriving on time using the MPTS.

Therefore, the probability of arriving on time is higher using the MPTS than using personal vehicles, so choice B is correct. The other choices are incorrect based on this analysis.

Due to Excessive Pollution, GREEN Solutions Inc