The temperature is recorded at 60 random airports in the United States. The average temperature is 76 degrees Fahrenheit, with a standard deviation of 9 degrees. Calculate and interpret the z-score corresponding to an airport temperature of 78 degrees Fahrenheit.
To calculate the z-score corresponding to an airport temperature of 78 degrees Fahrenheit, we can use the formula:
\[ z = \frac{x - \mu}{\sigma} \]
Where:
- x = the temperature of the airport (78 degrees Fahrenheit)
- μ = the average temperature (76 degrees Fahrenheit)
- σ = the standard deviation (9 degrees)
Plugging in the values, we get:
\[ z = \frac{78 - 76}{9} = \frac{2}{9} \approx 0.2222 \]
Therefore, the z-score corresponding to an airport temperature of 78 degrees Fahrenheit is approximately 0.2222.
Interpretation:
A z-score of 0.2222 indicates that the temperature at the airport of 78 degrees Fahrenheit is approximately 0.2222 standard deviations above the average temperature of 76 degrees Fahrenheit. This means that the temperature at this airport is slightly warmer than the average temperature across all the airports in the United States.