Question

7 customers enter a clothing store and are observed to determine if they will make a purchase. The store owner states that there is a 75% chance of a customer making a purchase. The random variable x represents a customer making a purchase. What is the probability that more than 3 customers make a purchase?

Answer 1

Solution

Given that ,

p = 75% = 0.75

1 - p = 0.25

n = 7

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X > 3) = P(X = 4) +  P(X = 5) + P(X = 6) + P(X = 7)

= (₇ C ₄) * 0.75⁴ * (0.25)³ + (₇ C ₅) * 0.75⁵ * (0.25)² + (₇ C ₆) * 0.75⁶ * (0.25)¹ + (₇ C ₇) * 0.75⁷ * (0.25)⁰

= 0.9294

Probability = 0.9294