Question

1. Sixty percent of all shoppers in a given shopping center use credit cards for their purchases. If 20 shoppers make purchases, find the probability that:

A). exactly 12 use credit cards.

B). exactly 7 do not use credit cards.

C). At most 10 use credit cards

D.) More than 13 use credit cards

Answer 1

Answer:

Given,

p = 60% = 0.6

sample n = 20

mean = np = 20*0.6 = 12

standard deviation = sqrt(npq) = 2.19

Binomial distribution P(X = r) = nCr*p^r*q^(n-r)

nCr = n!/(n-r)!*r!

a)

P(X = 12) = 20C12*0.6^12*(0.4)^(20-12)

= 125970*0.6^12*0.4^8

= 0.1797

b)

P(X = 7) = 20C7*0.6^7*0.4^(20-7)

= 77520*0.6^7*0.4^13

= 0.0146

exactly 7 do not use credit cards = 1 - P(x = 7)

= 1 - 0.0146

= 0.9854

c)

P(X <= 10) = P((x-u)/s < (10 - 12)/2.19)

= P(z < -0.91)

= 0.1814113 [since from z table]

= 0.1814

d)

P(X > 13) = P((x-u)/s > (13 - 12)/2.19)

= P(z > 0.46)

= 0.3227581 [since from z table]

= 0.3228