Question 854293: The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a s=15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be:
Z = (score-mean)/SD
a. Longer than 80 minutes?
z(80) = (80-60)/15 = 4/3
P(x> 80) = P(z> 4/3) = normal cdf(4/3,100) = 0.0912
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b. Less than 50 minutes?
z(50) = (50-60)/15 = -2/3
P(x< 50) = P(z< -2/3) = normal cdf(-100,-2/3) = 0.2525
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c. Between 45 and 75 minutes?
z(45) = (45-60)/15 = 41
z(75) = (75-60)/15 = 71
P (x=60) = P(z= ) = normal cdf (-100, ) =
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
using TI Calculator
mean = 60, Sd = 15
a. P(x> 80) = 1 - invNorm(area to left of desired z) = 1 - invNorm(4/3) = .0912
b. P(x< 50) = invNorm(area to left of desired z) = invNorm(-2/3) = .2525
c.P(45≤ x ≤ 75)= normalcdf(smaller, larger, µ, σ) = normalcdf(45,75,60,15)
or
P(45≤ x ≤ 75) = invNorm(1) - invNorm(-1) = .6827
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