Use the normal approximation to the binomial to find that probability for the specific value of X. n = 30, p = 0.4, X = 5?

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  • 2 weeks ago

    The probability of a specific value of the normal distribution is 0.  In order to use it to approximate the binomial distribution, we will need to consider a range of values, say from 4.5 to 5.5 and compute the probability over the range.

    The mean of the binomial distribution = np = 30(0.4) = 12

    The variance of the binomial distribution = np(1-p) = 30(0.4)(0.6) = 7.2

    The standard deviation is the square root of the variance = 2.68

    Lower z score = (4.5 - 12) / 2.68 = -2.80

    Upper z score = (5.5 - 12) / 2.68 = -2.43

    P(Z between these values) = about 0.005.

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