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A binomial random variable X has mean 6 and variance 2. The probability that 5 ≤ X ≤ 7 is
- 4/2
- 1622/6661
- 4672/6561
- none
Correct answer: 4672/6561
Solution
The mean and variance of a binomial random variable are related to the number of trials and the probability of success. Given the mean of 6 and variance of 2, we can determine the parameters of the binomial distribution and calculate the probability for the specified range, leading to the correct answer of 4672/6561.
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