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.)

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

Step-by-step 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

step-by-step explanation: