Shen, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Shen models the boulders' weights using a normal distribution with a mean of 565 kg and a standard deviation of 150 kg. Use this table or the ALEKS calculator to find the percentage of boulders that weigh between 733 kg and 859 kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

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**Boulder Weight Analysis for Highway Safety**

Shen, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Shen models the boulders' weights using a normal distribution with a mean of 565 kg and a standard deviation of 150 kg.

**Task:**
Use [this table](#) or the ALEKS calculator to find the percentage of boulders that weigh between 733 kg and 859 kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example, 98.23%).

### Instructions:
- First, identify the mean \( \mu = 565 \) kg and standard deviation \( \sigma = 150 \) kg of the normal distribution.
- Use the Z-score formula to find the Z-scores for 733 kg and 859 kg.
- Lookup the corresponding probabilities from the Z-table.
- Calculate the percentage of boulders falling within the given weight range.

![This is a text entry box for typing your answer. There are also buttons for confirming the answer, resetting, or asking for help.](#)


Feel free to utilize the specified tools for precise computation.
Transcribed Image Text:**Boulder Weight Analysis for Highway Safety** Shen, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Shen models the boulders' weights using a normal distribution with a mean of 565 kg and a standard deviation of 150 kg. **Task:** Use [this table](#) or the ALEKS calculator to find the percentage of boulders that weigh between 733 kg and 859 kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example, 98.23%). ### Instructions: - First, identify the mean \( \mu = 565 \) kg and standard deviation \( \sigma = 150 \) kg of the normal distribution. - Use the Z-score formula to find the Z-scores for 733 kg and 859 kg. - Lookup the corresponding probabilities from the Z-table. - Calculate the percentage of boulders falling within the given weight range. ![This is a text entry box for typing your answer. There are also buttons for confirming the answer, resetting, or asking for help.](#) Feel free to utilize the specified tools for precise computation.
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