### Understanding the Distribution of Animal Pregnancy LengthsThe lengths of a particular animal's pregnancies are approximately normally distributed with a mean (μ) of 280 days and a standard deviation (σ) of 12 days. Here are the questions to explore:1. **(a) What proportion of pregnancies lasts more than 295 days?** - **Solution Steps**: Calculate the Z-score for 295 days and use the standard normal distribution to find the proportion.2. **(b) What proportion of pregnancies lasts between 274 and 286 days?** - **Solution Steps**: Calculate the Z-scores for 274 and 286 days and determine the area between these values on the standard normal distribution.3. **(c) What is the probability that a randomly selected pregnancy lasts no more than 271 days?** - **Solution Steps**: Find the Z-score for 271 days and use it to determine the cumulative probability from the standard normal distribution.4. **(d) A "very preterm" baby is one whose gestation period is less than 262 days. Are very preterm babies unusual?** - **Solution Steps**: Calculate the Z-score for 262 days. If the probability is low, such occurrences are considered unusual.#### Interactive Learning- **Table of Areas**: A table of areas under the normal curve can be accessed by clicking the icon. This table will help find exact probabilities by providing the areas corresponding to different Z-scores.#### Problem Calculation- **Example**: Determining Proportions - **(a)** The proportion of pregnancies that last more than 295 days can be calculated by first finding the Z-score: - Z = (X - μ) / σ = (295 - 280) / 12 - Use the Z-score table to find the corresponding probability. - **Output**: (Results should be rounded to four decimal places.)This structured exploration of normal distribution will help understand how gestational periods compare to standard statistical expectations. Use statistical tools or tables for precise calculations.

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Answered: The lengths of a particular animal's…

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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The lengths of a particular animal's pregnancies are approximately normally distributed with a mean of 275 days and standard deviation of 20 days. What is the probability that a randomly selected pregnancy lasts no more than 240 days?

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