To find the temperature reading that separates the bottom 40.9% from the top 59.1%, we need to determine the z-score corresponding to the cumulative probability of 0.409, since the bottom 40.9% corresponds to a cumulative probability of 0.409 in the standard normal distribution.
We can use a z-table or statistical software to find the z-score.
Using a z-table, we look for the cumulative probability closest to 0.409. Let’s find the z-score:
- The z-score corresponding to a cumulative probability of 0.409 is approximately -0.23 (since the closest value in the table for 0.409 is 0.4099 which corresponds to -0.23).
Now we use the z-score formula to find the temperature \(X\):
\[ X = \mu + z \cdot \sigma \]
where:
- \(\mu = 0\) (mean)
- \(z \approx -0.23\)
- \(\sigma = 1\) (standard deviation)
Substituting in the values:
\[ X = 0 + (-0.23) \cdot 1 = -0.23 \]
Rounding this to the nearest hundredth, the temperature reading that separates the bottom 40.9% from the top 59.1% is:
\[ \boxed{-0.23} , \text{degrees Celsius} \]