To find the probability that a randomly selected day has a temperature below 73 degrees Fahrenheit, we can use the properties of the normal distribution. Given that the mean temperature (\( \mu \)) is 80 degrees and the standard deviation (\( \sigma \)) is 5 degrees, we first need to find the z-score for a temperature of 73 degrees:
The formula for the z-score is:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the value we are interested in (73 degrees),
- \( \mu \) is the mean (80 degrees),
- \( \sigma \) is the standard deviation (5 degrees).
Substituting the values:
\[ z = \frac{(73 - 80)}{5} = \frac{-7}{5} = -1.4 \]
Next, we look up the z-score of -1.4 in the standard normal distribution table, or we can use a calculator or statistical software to find the cumulative probability for \( z = -1.4 \).
The cumulative probability for \( z = -1.4 \) is approximately 0.0808, which is 8.08%.
Thus, the probability that a randomly selected day has a temperature below 73 degrees Fahrenheit is:
0 8.08%