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The 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, almost all (99.7%) of the students spent on textbooks in a semester:______.A. Between 230 and 240 dollars.B. Between 220 and 250 dollars.C. Between 175 and 295 dollars.D. Less than 220 dollars or more than 250 dollars.E. Less than 230 dollars or more than 240 dollars.

Respuesta :

Answer:

C. Between 175 and 295 dollars.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 235

Standard deviation = 20

According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:

Within 3 standard deviations of the mean.

235 - 3*20 = 175

235 + 3*20 = 295

So the correct answer is C.

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