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Math Help - Combinations of independant normal random variables

  1. #1
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    Combinations of independant normal random variables

    Ok a bit stuck with this 1.

    Monto sherry is sold in bottles of two sizes - standard and large. For each size, the content, in litres, of a randomly chosen bottle is normally distributed with mean and standard deviation as given in the table

    Mean Standard Deviation

    Standard Bottle 0.760 0.008
    Large Bottle 1.010 0.009

    i) I have already worked out that the probability of a randomly chosen standard bottle contains less than 0.750 litres is 0.1056.

    ii) Find the probability that a box of 10 randomly chosen standard bottles contains at least 3 bottles whose given contents are each less than 0.750 litres.
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  2. #2
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    Quote Originally Posted by djmccabie View Post
    Ok a bit stuck with this 1.

    Monto sherry is sold in bottles of two sizes - standard and large. For each size, the content, in litres, of a randomly chosen bottle is normally distributed with mean and standard deviation as given in the table

    Mean Standard Deviation

    Standard Bottle 0.760 0.008
    Large Bottle 1.010 0.009

    i) I have already worked out that the probability of a randomly chosen standard bottle contains less than 0.750 litres is 0.1056.

    ii) Find the probability that a box of 10 randomly chosen standard bottles contains at least 3 bottles whose given contents are each less than 0.750 litres.
    Let X be the random variable number of standard size bottles whose contents are less than 0.750 litres.

    X ~ Binomial(n = 10, p = 0.1056).

    Calculate \Pr(X \geq 3) = 1 - \Pr(X \leq 2).
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