Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)
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Answer:
81.85% of the workers spend between 50 and 110 commuting to work
Step-by-step explanation:
We can assume that the distribution is Normal (or approximately Normal) because we know that it is symmetric and mound-shaped.
We call X the time spend from one worker; X has distribution N(μ = 70, σ = 20). In order to make computations, we take W, the standarization of X, whose distribution is N(0,1)
The values of the cummulative distribution function of the standard normal, which we denote , are tabulated. You can find those values in the attached file.
Using the symmetry of the Normal density function, we have that . Hece,
The probability for a worker to spend that time commuting is 0.8185. We conclude that 81.85% of the workers spend between 50 and 110 commuting to work.