Each morning a man goes for a walk. He walks to the top a hill, and then walks d

Question

Each morning a man goes for a walk. He walks to the top a hill, and then walks down again. The time he takes to walk up the hill is normally distributed with µ = 20 (minutes) and = 3, whereas the time he takes to walk down the hill is normally distributed with µ = 15 and = 4. Assuming that the time taken for the uphill and downhill walks are independent, what is the probability that his walk will last: (a) between 35 and 40 minutes? (b) less than half an hour? What is the probability that the man will walk to the top of the hill quicker than he will walk down the hill?

Explanation / Answer

Let x be the variable denoting the uphill walk and y be the variable denoting the downhill walk.

Both the variables are normally distributed and are independent, hence the variable (X+Y) is also normally distributed.

X ~ (20, 9) and Y ~ (15,16) in the form of N(mu, sigma 2)

Hence Z = X+Y is distributed as Z (35, 25) i.e the variable is normally distributed with mean = 35, s.d = 5

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