MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Understanding Normal Distribution in Pregnancy Durations

The lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 17 days. 

**Problem Statement:**
What percentage of pregnancies last fewer than 314 days?

**Mathematical Expression:**

\[ P(X < 314 \, \text{days}) = P(Z < \frac{314 - 261}{17}) = P(Z < 3.12) \]

**Instructions:**
- Enter your answer as a percent accurate to 1 decimal place. Do not enter the "%" sign.

**Interactive Diagram Description:**

A normal distribution graph is displayed with a bell-shaped curve. The area under the curve to the left of approximately -0.8 is shaded in blue, representing the probability of pregnancies lasting fewer than 314 days.

**User Interaction:**
- Use the "Shade: Right of a value" slider to adjust the value and visualize other probabilities.

**Submit:**
- Click the "Submit Question" button once your answer is ready.

This exercise helps students understand how to apply the normal distribution and z-scores to real-world scenarios.
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Transcribed Image Text:### Understanding Normal Distribution in Pregnancy Durations The lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 17 days. **Problem Statement:** What percentage of pregnancies last fewer than 314 days? **Mathematical Expression:** \[ P(X < 314 \, \text{days}) = P(Z < \frac{314 - 261}{17}) = P(Z < 3.12) \] **Instructions:** - Enter your answer as a percent accurate to 1 decimal place. Do not enter the "%" sign. **Interactive Diagram Description:** A normal distribution graph is displayed with a bell-shaped curve. The area under the curve to the left of approximately -0.8 is shaded in blue, representing the probability of pregnancies lasting fewer than 314 days. **User Interaction:** - Use the "Shade: Right of a value" slider to adjust the value and visualize other probabilities. **Submit:** - Click the "Submit Question" button once your answer is ready. This exercise helps students understand how to apply the normal distribution and z-scores to real-world scenarios.
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