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Question 28

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?

The probability that they would arrive on time using personal vehicles is much higher than using the metro public transportation system (MPTS)

The probability that they would arrive on time using the MPTS is much higher than using their personal vehicles

The two probabilities are about the same excepting in one case the consistency is higher than the other

We need to compile more data around weekends to incorporate for traffic differences

When Standard Deviation is higher the probability goes down and so the MPTS is worse

Correct Answer: B

Given that the commute times follow a normal distribution, we can compare the probabilities using the Z-score formula. For personal vehicles, the mean commute time is 39 minutes with a standard deviation of 7 minutes. The Z-score for a 40-minute commute can be calculated as (40 - 39) / 7 ≈ 0.14. For the metro public transportation system, the mean commute time is 34 minutes with a standard deviation of 21 minutes. The Z-score for a 40-minute commute is calculated as (40 - 34) / 21 ≈ 0.29. Comparing these Z-scores using standard normal distribution tables, a Z-score of 0.14 indicates a higher probability of being on time than a Z-score of 0.29. Therefore, the probability of arriving on time is much higher using the metro public transportation system than using personal vehicles.

Discussion

MariaSCOption: E

shouldn't we know the sample size for X1 bar = 39, s = 7? we cannot perform Z test accurately, therefore we cannot decide if we accept H0 and with which probability. I am also voting for answer E. Makes more sense? please can someone confirm?

AhmednmOption: E

I shall go for E .. this is the most common sense answer for me .. it's better than A and C.. B definitely is wrong as well as D

minka292Option: C

Why not the answer C? I had the same question on my online training and the answer was C not B. I am confused now, could someone please confirm ? Thx