The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ = 473 and a standard deviation of: σ = 28. According to the standard deviation rule, almost 0.15% of the students spent more than what amount of money on textbooks in a semester?

0.15% of the students spent more than 557 on textbooks in a semester

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 = 473

Standard deviation = 28

According to the standard deviation rule, almost 0.15% of the students spent more than what amount of money on textbooks in a semester?

99.7% of the measures are within 3 standard deviations of the mean, so 100 - 99.7% = 0.3% are more than 3 standard deviations from the mean.

The normal distribution is symmetric, which means that 0.3%/2 = 0.15% spend less than 3 standard deviations below the mean, and 0.15% spend more than 3 standard deviations above the mean.

473 + 3*28 = 473 + 84 = 557

0.15% of the students spent more than 557 on textbooks in a semester

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step-by-step explanation: