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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 2.5% of the students spent more than what amount of money on textbooks in a semester? $195 $215 $235 $275 $295

Question

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of 235andastandarddeviationof235 and a standard deviation of 20. According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester? 195195 215 235235 275 $295

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Solution

According to the standard deviation rule, we can use the Z-score formula to find the amount of money that corresponds to the given percentage.

The Z-score formula is given by: Z = (X - μ) / σ

Where: Z is the Z-score X is the value we want to find μ is the mean σ is the standard deviation

In this case, we want to find the value of X that corresponds to the 2.5% percentile, which means we need to find the Z-score that corresponds to this percentile.

Using a Z-table or a calculator, we can find that the Z-score corresponding to the 2.5% percentile is approximately -1.96.

Now we can rearrange the Z-score formula to solve for X:

X = Z * σ + μ

Plugging in the values we have:

X = -1.96 * 20 + 235

Calculating this, we find:

X ≈ 195.2

Therefore, almost 2.5% of the students spent more than $195 on textbooks in a semester.

This problem has been solved

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