If the probability that an object dropped from a certain height will strike…
2024
If the probability that an object dropped from a certain height will strike the ground is 80% and 12 objects are dropped from the same place, find the mean and variance of the number that strike the ground.
Answer: A. 9.6, 1.92 — For a binomial distribution with n independent trials and success probability p, the number of successes X follows Binomial(n, p), where the mean is E(X) = np…
- A.
9.6, 1.92
- B.
8.6, 1.92
- C.
9.6, 1.82
- D.
8.6, 1.82
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Correct answer: A
For a binomial distribution with n independent trials and success probability p, the number of successes X follows Binomial(n, p), where the mean is E(X) = np and the variance is Var(X) = np(1 - p).
Identify the parameters from the question: n = 12 (objects dropped), p = 0.8 (probability an object strikes the ground), so q = 1 - p = 0.2.
Apply the mean formula: mean = np = 12 x 0.8 = 9.6.
Apply the variance formula: variance = np(1 - p) = 9.6 x 0.2 = 1.92.
Cross-check: variance can also be written as mean x q, so 9.6 x 0.2 = 1.92 again, confirming the two values are consistent with each other.