Question

The distribution of the annual incomes of a group of middle-management employees at Compton Plastics approximates a normal distribution with a mean of $47,200 and a standard deviation of $800.

1. About 68% of the incomes lie between what two amounts?
2. About 95% of the incomes lie between what two amounts?
3. About 99.7% of of the incomes lie between what two amounts?
4. What are the median and the modal incomes?

Answer 1

solution

Using Empirical rule,

(A)P( - 1< X < + 1) = 68%

P(47200 - 800 < X < 47200 +800) = 68%

P(46400 < X < 48000) = 68%

Answer =46400 and 48000

(B)

P( - 2< X < + 2) = 95%

P(47200 - 1600 < X < 47200 +1600) = 95%

P(45600 < X < 48800) =95%

Answer =45600 and 48800

(C)

P( - 3< X < + 3) = 99.7%

P(47200 - 2400 < X < 47200 +2400) = 99.7%

P(44800< X < 49600) =99.7%

Answer =44800 and 49600