Question

The monthly income of 5,000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1,250 and the standard deviation is $250. a) How many workers earn more than $1500 per month? b) How many workers earn less than $750 per month? c) What percentage of the workers earn between $750 and $1500 per month? d) What percentage of the workers earn less than $1750 per month?

Answer 1

Answer:

a) 15.86

b) 2.28%

c) 81.86%

d) 97.72%

Explanation:

we normalize to N(1;0)

Z = (X -u)/o

being u the mean

and o the standard deviation

a)

Z (1 - (1500 - 1250)/250) = 0.158655254

b)

Z (750-1250)/250 = 0.022750132

c)

Z ((1500 - 1250)/250) - Z (750) = 0.841344746 - 0.022750132 =

0.818594614

d)

Z (1750 - 1500)/250 = 0.977249868