A study of the amount of time it takes a hiker to hike to the bottom of the Grand Canyon and back to the top shows that the mean is 12 hours and the standard deviation is 2.4 hours. If 9 hikers are randomly selected, find the probability that their mean hiking time is less than 10.8 hours. P(x<10.8 hours = P (z <

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A study of the amount of time it takes a hiker to hike to the bottom of the Grand Canyon and back to the top shows that the mean is 12 hours and the standard deviation is 2.4 hours. If 9 hikers are randomly selected, find the probability that their mean hiking time is less than 10.8 hours.

\[ P(x < 10.8 \text{ hours}) \]

\[ = P(z < \) 

Shade the appropriate region. Be sure to round your previous answer to one decimal place in order to graph:

Shading: Left of a value. Click and drag the arrows to adjust the values.

---

**Image Description:**

The picture includes a breathtaking view of the Grand Canyon, highlighting its vibrant stratified layers. Below the image is a graph with a bell curve, representing a normal distribution. The graph is intended for shading the area representing the probability calculated for the hikers' mean hiking time.
Transcribed Image Text:A study of the amount of time it takes a hiker to hike to the bottom of the Grand Canyon and back to the top shows that the mean is 12 hours and the standard deviation is 2.4 hours. If 9 hikers are randomly selected, find the probability that their mean hiking time is less than 10.8 hours. \[ P(x < 10.8 \text{ hours}) \] \[ = P(z < \) Shade the appropriate region. Be sure to round your previous answer to one decimal place in order to graph: Shading: Left of a value. Click and drag the arrows to adjust the values. --- **Image Description:** The picture includes a breathtaking view of the Grand Canyon, highlighting its vibrant stratified layers. Below the image is a graph with a bell curve, representing a normal distribution. The graph is intended for shading the area representing the probability calculated for the hikers' mean hiking time.
Expert Solution
Step 1

Given:

μ = 12

σ = 2.4

n = 9

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