Question 655186: The time patrons at the Grande Dunes Hotel in the Bahamas spend waiting for an elevator follows a uniform distribution between 0 and 3.5 minutes.
a.show that the area under the curve is 1.00.
b.How long does the typical patron wait for elevator service?
c.What is the standard deviation of the waiting time?
d.What fraction of the patrons wait for less than a minute?
e.What fraction of the patrons wait more than 2 minutes?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.)Find the area under the standard normal curve:
I. to the right of z = -2.32
Using a TI-84 I get: normalcdf(-2.32,100) = 0.9898
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II. to the left of z = -2.32
normalcdf(-100,-2.32) = 0.0102
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2.) Assume that the population of heights of male college students is approximately normally distributed with mean m of 70 inches and standard deviation s of 3.75 inches. Show all work.
(A) Find the proportion of male college students whose height is greater than 68 inches.
z(68) = (68-70)/3.75 = -0.5333
P(x > 68) = P(z > -0.5333) = 0.7031
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2) Find the proportion of male students whose height is less than 68
Ans: 1 - 0.7031 = 0.2969
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3.) The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.5 inches and a standard deviation of 0.50 inches. Show all work.
(A) What percentage of the grapefruits in this orchard have diameters less than 6.3 inches?
z(6.3) = (6.3-6.5)/0.5 = -0.4
P(x < 6.3) = P(z < -0.4) = normalcdf(-100,-0.4) = 0.3446
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(B) What percentage of the grapefruits in this orchard are larger than 6.15 inches?
z(6.15) = (6.15-6.5)/0.5 = 0.7
P(x > 6.15) = P(z > 0.7) = 0.2420
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Cheers,
Stan H.
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