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Find the mean and standard deviation of the binomial distribution for which n = 40 and p = 0.2.

User RoboKozo
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Final answer:

To find the mean (μ) and standard deviation (σ) of a binomial distribution with n = 40 and p = 0.2, use the formulas μ = np for the mean and σ = √(npq) for the standard deviation. This gives a mean of 8 and a standard deviation of approximately 2.53.

Step-by-step explanation:

The question is asking about finding the mean and standard deviation for a binomial distribution with a given number of trials (n) and probability of success (p). Specifically, n = 40 and p = 0.2.

First, we calculate the mean, which is given by the formula μ = np. In this case:

  • μ = (40)(0.2) = 8

Next, we calculate the standard deviation, which is the square root of the variance. The variance is calculated using the formula σ² = npq, where q is the probability of failure (1 - p).

  • σ² = (40)(0.2)(1 - 0.2)
  • σ² = 40(0.2)(0.8)
  • σ² = 6.4
  • σ = √6.4 ≈ 2.5298

Hence, for n = 40 and p = 0.2, the binomial distribution has a mean of 8 and a standard deviation of approximately 2.53.

User Raveesh Sharma
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