Question

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.

Answer 1

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