Question

The mean temperature during the summer in a certain city is 80 degrees Fahrenheit, with a standard deviation of 5 degrees Fahrenheit. What is the probability that a randomly selected day has a temperature below 73 degrees Fahrenheit?

(1 point)
Responses

4.75%
4.75%

8.08%
8.08%

91.92%
91.92%

95.25
95.25

Answer 1

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.

We know:
- Mean (\(\mu\)) = 80 degrees Fahrenheit
- Standard deviation (\(\sigma\)) = 5 degrees Fahrenheit

We need to calculate the z-score for 73 degrees Fahrenheit using the formula:

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

where \(X\) is the value we are interested in (73 in this case).

Substituting the values:

\[
z = \frac{73 - 80}{5} = \frac{-7}{5} = -1.4
\]

Now, we will use the z-score to find the corresponding probability. You can use a standard normal distribution table or calculator to find the probability corresponding to \(z = -1.4\).

Using a z-table or calculator, the probability \(P(Z < -1.4)\) is approximately \(0.0808\).

To convert this to a percentage:

\[
0.0808 \times 100 = 8.08\%
\]

Thus, the probability that a randomly selected day has a temperature below 73 degrees Fahrenheit is **8.08%**.

The correct response is:

**8.08%**