Question: It is known that the household income of a small town
has a mean of $48,000 and a standard deviation of $12,000. Assuming
household income is normally distributed,
a. what percentage of the households earn more than
$84,000?
b. Solve the same problem by applying the empirical
rule. Provide a clear explanation.
Solution :
(a)
P(x > 84000) = 1 - P(x < 84000)
= 1 - P[(x - ) / < (84000 - 48000) / 12000]
= 1 - P(z < 3)
= 1 - 0.9987
= 0.0013
(b)
Using Empirical rule,
P( - 3< X < + 3) = 99.7%
P(x > 48000) = 0.0015
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