Answer:
Probability of more than 9 adult Australian sheep dogs out of 12 weighing 65 lb or more
P(X > 9) = 0.00788
Step-by-step explanation:
The only assumption required for the question is that all 12 adult dogs sampled must all be Australian sheep dogs.
This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of adult dogs to be sampled = 12
x = Number of successes required = number of dogs that weigh 65 lb or more
= more than 9; >9
p = probability of success = probability of a dog weighing 65 lb or more = 0.45
q = probability of failure = probability of a dog NOT weighing 65 lb or more = 1 - 0.45 = 0.55
P(X > 9) = P(X=10) + P(X=11) + P(X=12)
Solving each of these probabilities, using the binomial distribution formula
P(X = x) = ¹²Cₓ (0.45)ˣ (0.55)¹²⁻ˣ with x = 10, 11 and 12
P(X > 9) = P(X=10) + P(X=11) + P(X=12)
= 0.00679820806 + 0.00101130368 + 0.00006895252
= 0.00787846427
= 0.00788 to 3 s.f
Hope this Helps!!!
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