Problem

When Ella commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 34 minutes and a standard deviation of 4.5 minutes. Out of the 210 days that Ella commutes to work per year, how many times would her commute be between 28 and 38 minutes, to the nearest whole number?

Answer

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Answer

\( 210 \times 0.7267 \approx 152.61 \)

Steps

Step 1 ：\( P(28 < X < 38) = \Phi\left(\frac{38 - 34}{4.5}\right) - \Phi\left(\frac{28 - 34}{4.5}\right) \)

Step 2 ：\( P(28 < X < 38) \approx 0.7267 \)

Step 3 ：\( 210 \times 0.7267 \approx 152.61 \)

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