Question

g what is the approximate probability that in a random sample of 1000 individuals who have purchased fries at McDonald’s, at least 40 can taste the difference between the two oils? (2.5 pts.)

Answer 1

Probability that at least 40 can taste difference between two oils:

P(x ≥ 40) = p( x - µ / ∂ ≥ 39.5 – 30 / √29.1)

= p( z > 1.76)

= 1 – 0.9608

= 0.0392

Explanation:

Solution:

Given:

Random sample = n = 1000

Probability of people identify the taste = p = 0.03

Probability that people do not identify the taste is 0.97.

Since np = 1000 x 0.03 = 30

And

nq = n(1 – p) = 970

Verify the condition:

np ≥ 10

1000 x 0.03 ≥ 10

30 ≥ 10

And nq ≥ 10

1000 x 0.97 ≥ 10

970 ≥ 10

Hence conditions are satisfied, it is valid to apply normal approximation to binomial distribution.

µ = 30 and ∂ = √29.1

Probability that at least 40 can taste difference between two oils:

P(x ≥ 40) = p( x - µ / ∂ ≥ 39.5 – 30 / √29.1)

= p( z > 1.76)

= 1 – 0.9608

= 0.0392