intro to statistics

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a vending machine dispenses coffee into an 8 oz cup. the amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.03 oz.you can allow the cup to overfill 1 percent of the time. what among should you set as the mean amount of coffee to be dispensed?

  • intro to statistics -

    Using a normal distribution function, select the value of x(mean) that makes the probability integral of P(x) from x = 0 to 8.0 equal to 0.99, when sigma = 0.03

  • intro to statistics -

    You may find the JAVA tool at this website for problems of this type.
    http://psych-www.colorado.edu/~mcclella/java/normal/accurateNormal.html
    I used it to get an answer of 7.93 oz.
    Enter mean of 7.93, sigma = 0.03 and the range of P(x) 0 to 8.0 oz, and you get a probability of 0.990

  • intro to statistics -

    Use Norminv in excel(%, cup size, stanard dev ) then round to the 2nd decimal

    hope this helpful

  • intro to statistics -

    Find the z-value with a right tail of 1%: z = 2.3263
    -----------
    Find the x-value using x = zs+u
    x = 2.3263*0.01+8 = 8.0233
    ========
    Let that be the mean amount of coffee to be dispensed

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