The Zscore of a value x is the number of standard deviations

The Z-score of a value, x, is the number of standard deviations that x is from the mean. The formula is : Z = x-mu/sigma Important facts about Z-scores: When 2 is negative, then * Is below the mean; When Z is positive, then * is above the mean; When Z Is zero, then * is equal to the mean. The grocery store owner also rates her apples for quality. With apples, she uses a 100 point scale. Ten of her apple\'s ratings arc listed below. For this problem we will think of the apples as an entire population The population mean rating Is - 65.7 and the populate standard deviation for the ratings is o = 8.1. A Suppose that you apple with a rating of 84. How many standard deviations is this above average? B Interpret this Z-score in context. Compare apples to oranges! Which is better - the orange with a rating of 18, or the apple with a rating of 84?

Solution

A)

z = (x - u)/sigma = (84 - 65.7)/8.1 = 2.259259259 [ANSWER]

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b)

This means that this apple is 2.259 standard deviations above the average apple\'s rating.

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c)

Hi! Please resubmit this problem together with the data regarding oranges. Those data are not included here. Please also indicate which parts are done already.

As a general instruction, please compare which has a greater z score: an orange of rating 18, or an apple of rating 84? That will be the better one.