Sergio’s job is just a few bus stops away from his house. While it can be faster to take the bus to work, it’s more variable, because of variations in traffic. He estimates that the commute time to work by bus is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes. The commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with a standard deviation of 1 minute. What is the probability that the bus will be faster than walking?

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sqdancefan sqdancefan · Answer 1 · 2020-12-25T04:56:56+01:00

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Answer:

A. 0.8340

Step-by-step explanation:

The mean difference between walking time and bus time is the difference of their means: 16 -12 = 4 minutes.

The variance of the difference between walking time and bus time is the sum of the variances of the two distributions:

(4 min)² +(1 min)² = 17 min²

Then the probability that walking will be slower is the probability that the difference is greater than 0.

P(dif > 0) = P(Z > (0 -4)/√17) = P(Z > -0.970143)

P(dif > 0) ≈ 0.8340

The probability the bus will be faster is about 0.8340.