Assistance on probability

Question

A business has Brand A, Brand B and Brand C of the same product. Market research has shown that 43% of costumers that purchase this product will choose Brand A. An organization conducts a poll of 100 consumers. Find the probability that 40 to 45 of the 100 consumers will prefer Product A, given the 43% brand preference is correct.

Answer 1

x = number of consumers- want to find: P(40 < x < 45)

z = (x - np)/sqrt(npq) has standard normal distribution.

n = 100, p = 0.43, q = 1 - 0.43 = 0.57

np = 100* 0.43 = 43

sqrt(npq) = sqrt(100*0.43*0.57) = 4.95

convert P(40 < x < 45) to z:

P( (40-43)/4.95 < z < (45-43)/4.95)

= P(-0.61 < z < 0.40)

= P(z < 0.40) - P(z < -0.61)

= 0..6554 - 0.2709 = 0.3845