Answer:
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
