Questions: During ski season, the resort town of Valhalla sees a daily mean snowfall of 5.3 inches with a standard deviation of 1.7. Use the Z-Scores Table to determine how many of the 201 days of ski season Valhalla should expect less than 2.2 inches of snow.

Solution Steps

To determine how many days Valhalla should expect less than \(2.2\) inches of snow, we first calculate the Z-score using the formula:

\[ z = \frac{X - \mu}{\sigma} \]

where:

• \(X = 2.2\) (the value we are interested in),
• \(\mu = 5.3\) (the mean snowfall),
• \(\sigma = 1.7\) (the standard deviation).

Substituting the values, we have:

\[ z = \frac{2.2 - 5.3}{1.7} = \frac{-3.1}{1.7} \approx -1.8235 \]

Thus, the Z-score for \(2.2\) inches of snow is approximately \(-1.8235\).

Next, we refer to the Z-score table to find the area to the left of \(z = -1.8235\). From the table, we find that the area (probability) corresponding to this Z-score is approximately \(0.0346\).

To find the expected number of days with less than \(2.2\) inches of snow, we multiply the probability by the total number of days in the ski season:

\[ \text{Expected Days} = \text{Probability} \times \text{Total Days} = 0.0346 \times 201 \approx 7 \]

Final Answer