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  1. #1
    Amy
    Amy is offline
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    Statistics Help

    Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. If you select a random sample of 25 bottles what is the probability that the sample mean will be:
    a. Between 1.99 and 2.0 liters
    .
    b The probability is 99% that the sample mean will contain at least how much soft drink?

    c. The probability is 99% that the sample mean will contain an amount that is between which two values (symmetrically distributed around the mean)?

    For the first one I got the ans 0.0793
    The last two I didn't understand, the questions.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Amy View Post
    Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. If you select a random sample of 25 bottles what is the probability that the sample mean will be:
    a. Between 1.99 and 2.0 liters
    The standard deviation of the mean of a sample of size 25 will be:

    sigma=0.05/sqrt(25)=0.01.

    A fill of between 1.99 and 2.0, is from z-score -1, to 0, and:

    p(-1<z<0)= 0.3413

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Amy View Post
    Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. If you select a random sample of 25 bottles what is the probability that the sample mean will be:

    b The probability is 99% that the sample mean will contain at least how much soft drink?
    The z-score x such that p(z<x)=0.01 is ~-2.33, so the fill that will give us
    this z-score is y:

    -2.33 = (y-2.0)/0.01, or y~=1.9977 litres

    RonL
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