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.(1 point)

Responses

The temperature is 2 standard deviations above the mean.
The temperature is 2 standard deviations above the mean.

The temperature is 0.222 standard deviations above the mean.
The temperature is 0.222 standard deviations above the mean.

The temperature is 2 standard deviations below the mean.
The temperature is 2 standard deviations below the mean.

The temperature is 0.222 standard deviations below the mean.

1 answer

To calculate the z-score for a temperature of 78 degrees Fahrenheit, you can use the following formula:

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

where:

\( X \) is the value of interest (78 degrees),
\( \mu \) is the mean (76 degrees),
\( \sigma \) is the standard deviation (9 degrees).

Now, plug in the values:

\[ z = \frac{(78 - 76)}{9} = \frac{2}{9} \approx 0.222 \]

Thus, the z-score corresponding to an airport temperature of 78 degrees Fahrenheit is approximately 0.222.

Interpretation: This means that a temperature of 78 degrees Fahrenheit is about 0.222 standard deviations above the mean temperature of 76 degrees Fahrenheit.

So the correct response is:

The temperature is 0.222 standard deviations above the mean.