Respuesta :
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)
[tex] W = \frac{X-μ}{σ} = \frac{X-70}{20} [/tex]
The values of the cummulative distribution function of the standard normal, which we denote [tex] \phi [/tex] , are tabulated. You can find those values in the attached file.
[tex]P(50 < X < 110) = P(\frac{50-70}{20} < \frac{X-70}{20} < \frac{110-70}{20}) = P(-1 < W < 2) = \\\phi(2) - \phi(-1)[/tex]
Using the symmetry of the Normal density function, we have that [tex] \phi(-1) = 1-\phi(1) [/tex] . Hece,
[tex]P(50 < X < 110) = \phi(2) - \phi(-1) = \phi(2) - (1-\phi(1)) = \phi(2) + \phi(1) - 1 = \\0.9772+0.8413-1 = 0.8185[/tex]
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.
