A survey asks 1200 workers, "has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-five percent of those survey selected. The random variable represents the number of workers who are reducing the amount of vacation. Find the mean, variance and standard deviation of the binomial deviation of the binomial distribution.

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Rodriguez

Mathematics

16 January, 07:36

A survey asks 1200 workers, "has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-five percent of those survey selected. The random variable represents the number of workers who are reducing the amount of vacation. Find the mean, variance and standard deviation of the binomial deviation of the binomial distribution.

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Ashanti Monroe · Answer 1

If a variable is binomially distributed with n trials and a success probability of p, then the mean = np, variance = np (1-p) and standard deviation = square root of variance.

In this case, n = 1200, p = 0.35. So, mean = (1200) (0.35) = 420,

variance = (1200) (0.35) (1-0.35) = 273,

standard deviation = square root of variance = √273 = 16.52.