He distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

Question

Mathematics

Gracie Odonnell

9 May, 01:40

He distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

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Edith · Answer 1

The standard deviation rule tells us that for distributions that have the normal shape, approximately 99.7% of the observations fall within 3 standard deviations of the mean.

Here, Mean = 235 and Standard deviation = 20

So, 3 standard deviation below the mean = Mean - 3 standard deviation

= 235 - (3 * 20)

= 235 - 60 = 175

and 3 standard deviation above the mean = Mean + 3 standard deviation

= 235 + (3 * 20)

= 235 + 60 = 295

So, almost all (99.7%) of the students spent between $175 and $295 on textbooks in a semester.