According to the U.S. Department of Labor, the average American household spends
ID: 3132197 • Letter: A
Question
According to the U.S. Department of Labor, the average American household spends $639 on household supplies per year. Suppose annual expenditures on household supplies per household are uniformly distributed between the values of $257 and $1,021. What is the standard deviation of this distribution? What is the height of this distribution? What proportion of households spend more than $890 per year on household supplies? What proportion of households spend more than $1,210 per year on household supplies? What proportion of households spend between $350 and $470 on household supplies? (Round your answers to 4 decimal place.) Standard deviation = Height = P(x > 890) = P(x > 1,210) = P(350Explanation / Answer
a)
Note that here,
a = lower fence of the distribution = 257
b = upper fence of the distribution = 1021
Hence,
s^2 = variance = (b -a)^2 / 12 = 48641.33333
Thus,
s = standard deviation = sqrt(s^2) = 220.5478028 [ANSWER]
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b)
h = 1/(b-a) = 1/(1021-257) = 0.001308901 [ANSWER]
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c)
Note that here,
a = lower fence of the distribution = 257
b = upper fence of the distribution = 1021
Note that P(x>c) = P(c<x<b) = (b-c)/(b-a). Thus, as
c = critical value = 890
Then
P(x>c) = 0.171465969 [ANSWER]
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d)
As the distribution is only from 257 to 1021, then it could no way be >1210.
Hence,
P(x>1210) = 0 [ANSWER]
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E)
Note that here,
a = lower fence of the distribution = 257
b = upper fence of the distribution = 1021
Thus, the area between the said numbers is
c = lower number = 350
d = higher number = 470
Thus, the probability between these two values is
P = (d - c)/(b - a) = 0.157068063 [ANSWER]
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