### Understanding Normal Distribution in Pregnancy DurationsThe 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.

Given: The corresponding Z score can be calculated as: The probability that the length of…

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. What percentage of pregnancies last fewer than 314 days? P(x < 314 days) = P(z<

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. What percentage of pregnancies last fewer than 314 days? P(x < 314 days) = P(z<

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### 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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