Question

A major department store has determined that its customers charge an average of $500 per month, with a standard deviation of $80. Assume the amounts of charges are normally distributed. (Round your answers to two decimal places.)

(a)

What percentage of customers charges more than $340 per month?

(b)

What percentage of customers charges less than $380 per month?

(c)

What percentage of customers charges between $604 and $660 per month?

Answer 1

Solution :

Given that ,

mean = = $500

standard deviation = = $80

a) P(x > $340) = 1 - P(x < 340)

= 1 - P[(x - ) / < (340 - 500) / 80)

= 1 - P(z < -2)

= 1 - 0.0228 = 0.9772

Percentage = 97.72%

b) P(x < $380) = P[(x - ) / < (380 - 500) / 80]

= P(z < -2)

= 0.0228

Percentage = 2.28%

c) P($604 < x < $660) = P[(604 - 500)/ 80) < (x - ) /  < (660 - 500) /80 ) ]

= P(1.3 < z < 2)

= P(z < 2) - P(z < 1.3)

= 0.9772 - 0.9032

0.074

Percentage = 7.40