Statistiscs

Students in the psychology department consume an average of 5 cups of coffee per day with a standard deviation of 1.75 cups. The number of cups of coffee consumed is normally distributed.

• What proportion of students consume an amount equal to or less than 6 cups a day?

• How many cups would an individual at the 80th percentile drink?

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  1. Use z-scores.

    Formula:
    z = (x - mean)/sd

    In the first part, find z.
    z = (6 - 5)/1.75
    Calculate, then use a z-table to find the proportion.

    In the second part, find z using a z-table for the 80th percentile. Plug into the formula, along with mean and standard deviation. Solve for x.

    I hope this will help get you started.

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  2. z = (6 - 5)/1.75 = 0.57
    .2157+.50= 0.7157x100=71.57%

    i.e 71.57%
    In the second part, find z using a z-table for the 80th percentile. Plug into the formula, along with mean and standard deviation. Solve for x.
    z = (x - mean)/sd
    z (sd)= X-mean
    z (sd)+mean= X
    0.20= (X-5)/0.57
    (0.20 x 0.57)+ 5= 5.11

    b)= 5.11?
    The closest in the table for 80th percentile is z=0.20 or 0.21 if I am looking at the right place? Is the above correct by any chance?
    Thanks

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