Answer:
Explanation:
We would apply the formula for binomial distribution. It is expressed as
P(x = r) = nCr × q^(n - r) × p^r
Where
n = number of samples
p = probability of success.
q = probability of failure
From the information given,
n = 12
p = 90% = 90/100 = 0.9
q = 1 - p = 1 - 0.9 = 0.1
28) Probability that at least 10 are ripe within 4 days is expressed as
P(x ≥ 10) = P(x = 10) + P(x = 11) + P(x = 12)
P(x = 10) = 12C10 × 0.1^(12 - 10) × 0.9^10 = 0.23
P(x = 11) = 12C11 × 0.1^(12 - 11) × 0.9^11 = 0.38
P(x = 12) = 12C12 × 0.1^(12 - 12) × 0.9^12 = 0.28
P(x ≥ 10) = 0.23 + 0.38 + 0.28 = 0.89
29) Probability that no more than 9 are ripe within 4 days is expressed as
P(x ≤ 9) = 1 - P(x ≥ 10)
P(x ≤ 9) = 1 - 0.89 = 0.11