Question 1081509: A large coffee is on average 563 mL, with a standard deviation of 1.4 mL. Rebecca measures the amount of liquid in her coffee and finds that it contains exactly 559.3 mL of coffee. On any given day, the place sells an average of 1000 large coffees. What number of coffees would have less coffee than her coffee?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
average size is 563 ml.
standard deviation is 1.4 ml.
distribution is assumed to be normal.
her z-score is equal to (x-m)/s
x is the amount of coffee she has in her cup.
m is the average amount in each cup every day.
s is the standard deviation of the distribution of amounts of coffee in each cup every day.
z-score is therefore equal to (559.3-563)/1.5 = -2.467 which can be rounded to -2.47.
if you look into the z-score tables, you will find that .0068 of the area under the normal distribution curve is to the left of a z-score of -2.47
this indicates that only .68% of the people who buy large coffees at this place got less coffee in their cup than she did.
since there are, on average 1000 people who buy coffee at this store every day, then .0068 * 1000 = 6.8 people get less liquid in their coffee than she did on average every day.
that's roughly equal to 7 if you round up to the nearest integer.
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