a. What percentage of sales are greater than $13,000? b. What percentage of sales are less than $8,000? c. What percentage of sales are between $8,000 than $12,000?

Question

1.      The sales in a store are normally distributed with a mean of $10,000 and a standard deviation of $2000.

a.      What percentage of sales are greater than $13,000?     

b.     What percentage of sales are less than $8,000?   

c.      What percentage of sales are between $8,000 than $12,000?  

Answer 1

x = amount of sales

use normalized z stat = (x - mean)/SD = (x - 10000)/2000

a) want to find P(x > 13000)

convert lower limit 13000 to normalized z stat

z = (13000 - 10000)/2000 = 1

P(x >13000) = P(z > 1) = 1 - P(z < 1)

look up probability in standard normal probability table

b) want to find P(x < 8000)

convert upper limit 8000 to normalized z stat as in part a)

c) P(8000 < x < 12000)

convert lower and upper limits to normalized z stat as in parts a) and b)