Explore BrainMass

Explore BrainMass

    Normal approximation to binomial distribution

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    It is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are

    a) less than 120 yellow beans
    b) between 120 and 150 yellow beans (inclusive)
    c) more than 160 yellow beans

    © BrainMass Inc. brainmass.com June 3, 2020, 5:00 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/normal-approximation-binomial-distribution-10714

    Solution Preview

    Let X be the no. of yellow beans

    X ~ Bin (400, 0.35)

    Since n is large, p is not too small, such that
    np = 140
    npq = 260

    We use normal approximation to binomial distribution.

    Therefore X~N (140, 91) approx Note: X~N (np, npq)

    a) P(x < 120) = P(x < 119.5)

    ...

    Solution Summary

    The solution discusses that it is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are

    a) less than 120 yellow beans
    b) between 120 and 150 yellow beans (inclusive)
    c) more than 160 yellow beans

    $2.19

    ADVERTISEMENT