Question

The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly 7 of the 10 Coffleton residents recognize the brand name.

0.0824

0.156

0.000806

0.0850

Answer 1

0.156

Explanation:

Using binomial probability formula, we have :

P( a out of n ) =ⁿCₐ x pᵃ x qⁿ⁻ᵃ ------------------------------------------------- (1)

Where n = total number of sample

a = number of success

p = probability of success

q = probability of failure

n-a = number of failures

From the question:

n =10 , a = 7, p=0.54, q = 1-p = 0.46

Substituting into equation (1) we have:

P (7 out of 10) = ¹⁰C₇ x (0.54)⁷x (0.46)¹⁰⁻⁷

= 0.1563

≈ 0.156