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    • Thread Starter

    This is a relatively simple question taken from the January 2005 MS/SS1B paper that I am kind of struggling with..

    4) Chopped lettuce is sold in bags nominally containing 100 grams.

    The weight, X grams of chopped lettuce, delivered by the machine filling the bags, may be assumed to be normally distributed with the mean M and standard deviation 4.

    b) Determine the minimum value of M so that at most 2% of the bags of chopped lettuce are underweight. Give your answer to one decimal place.

    c) Boxes each contain 10 bags of chopped lettuce. The mean weight of a bag of chopped lettuce in a box is denoted by (X bar).

    Given that M = 108.5

    i) Write down values for the mean and variance of (X bar)

    ii) Determine the probability that (X bar) exceeds 110.

    Any help would be truly appreciated!

    X~N(m, (4^2))

    a) P(X<100)=0.02

    * Z=(1/s)(X-m)


    The actual z-score is less than 0.5, there fore the z-value must lie to the left of the mean of the distribution.


    By linear interpolation betweeen the values of z=1.96 and z=2.3263





    c) x_=108.5g=>Var(x_)=(8.5^2)=72.25

    =>X~N(108.5, (8.5^2))

    * Z=(1/s)(X-m)



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Updated: May 17, 2005

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