SOLUTION: The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed. a. Suppose you l

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Question 1093775: The average annual amount American households spend for daily transportation is $6312
(Money, August 2001). Assume that the amount spent is normally distributed.
a. Suppose you learn that 5% of American households spend less than $1000 for daily
transportation. What is the standard deviation of the amount spent?
b. What is the probability that a household spends between $4000 and $6000?
c. What is the range of spending for the 3% of households with the highest daily transportation
cost?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The average annual amount American households spend for daily transportation is $6312
Note: That tells you the mean is 6312.
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(Money, August 2001). Assume that the amount spent is normally distributed.
a. Suppose you learn that 5% of American households spend less than $1000 for daily transportation. What is the standard deviation of the amount spent?
Find the z-value with a left tail of 5%::
invNorm(0.05) = -1.645
Note:: x = z*s + u
Solve for "s"::
1000 = -1.645*s + 6312
s = (1000-6312)/-1.645 = $3229.18
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b. What is the probability that a household spends between $4000 and $6000?
z(4000) = (4000-6312)/3229.18 = -0.7160
z(6000) = (6000-6312)/3229.18 = -0.0966
Ans: P(4000<= x <=6000) = P(-0.7160<= z <= -0.0966) = 0.2245
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c. What is the range of spending for the 3% of households with the highest daily transportation costs.
Find the z-value with a left-tail of 97%
invNorm(0.97) = 1.8808
Find the corresponding cost::
x = 1.8808*3229.18+6312 = $12385.42
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Cheers,
Stan H.
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