SOLUTION: An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.

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Question 647788: An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.

a. In what percent of the days will it take him 30 or fewer minutes to reach his office?

b. What percent of the days will it take between 40 and 50 minutes?

c. What percent of days will it take him between 30 and 45 minutes?

d. How long will the longest 10% of the trips take?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.
a. In what percent of the days will it take him 30 or fewer minutes to reach his office?
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z(30) = (30-35)/8 = -5/8
P(x <= 30) = P(z <= -5/8) = normalcdf(-100,-5/8) = 0.2660 = 26.60%
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b. What percent of the days will it take between 40 and 50 minutes?
Find the z-scores.
Find the percentage between those z-scores.
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c. What percent of days will it take him between 30 and 45 minutes?
Same procedure as on "b".
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d. How long will the longest 10% of the trips take?
Find the z-value with a left tail of 0.90
invNorm(0.9) = 1.2815
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x = zs + u
x = 1.2815*8+35 = 45.25
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Cheers,
Stan H.