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(g) What is the cutoff number of days for a pregnancy for the bottom 20% of women?

(g) What is the cutoff number of days for a pregnancy for the bottom 20% of women?

MATLAB: An Introduction with Applications
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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Question G

### Understanding Pregnancy Duration and Probability The lengths of pregnancies are normally distributed with a mean of 280 days and a standard deviation of 16 days. The following problems help us explore probabilities related to the length of pregnancies. #### Questions: (a) **Probability of Shorter Pregnancy:** - Find the probability that an individual woman has a pregnancy shorter than 271 days. (b) **Probability for a Sample Mean:** - If 25 women are randomly selected, find the probability that they have a mean pregnancy shorter than 271 days. (c) **Methodological Differences:** - There should be a difference in your method for the previous two questions. Explain what you did differently for each problem and explain WHY your answers are different. (d) **Probability of Longer Pregnancy:** - Find the probability that an individual woman has a pregnancy longer than 300 days. (e) **Probability of Pregnancy Between Two Values:** - Find the probability that an individual woman has a pregnancy between 280 and 300 days. (f) **Cutoff for the Top 15%:** - What is the cutoff number of days for a pregnancy for the top 15% of women? (g) **Cutoff for the Bottom 20%:** - What is the cutoff number of days for a pregnancy for the bottom 20% of women? #### Explanation of Approaches: - **Calculating Probabilities for Individuals vs. Samples:** - For individual probabilities (questions a and d), use the standard normal distribution with the given mean and standard deviation. - For sample means (question b), use the standard error to adjust the standard deviation, as the sample size affects variability. - **Interpreting Results:** - Understanding how the probabilities reflect population characteristics helps in statistical reasoning and decision-making. The cutoff points for specific percentiles (questions f and g) indicate how these values distribute across a population. This informs expectations for individual pregnancy durations compared to societal averages.
Transcribed Image Text:### Understanding Pregnancy Duration and Probability The lengths of pregnancies are normally distributed with a mean of 280 days and a standard deviation of 16 days. The following problems help us explore probabilities related to the length of pregnancies. #### Questions: (a) **Probability of Shorter Pregnancy:** - Find the probability that an individual woman has a pregnancy shorter than 271 days. (b) **Probability for a Sample Mean:** - If 25 women are randomly selected, find the probability that they have a mean pregnancy shorter than 271 days. (c) **Methodological Differences:** - There should be a difference in your method for the previous two questions. Explain what you did differently for each problem and explain WHY your answers are different. (d) **Probability of Longer Pregnancy:** - Find the probability that an individual woman has a pregnancy longer than 300 days. (e) **Probability of Pregnancy Between Two Values:** - Find the probability that an individual woman has a pregnancy between 280 and 300 days. (f) **Cutoff for the Top 15%:** - What is the cutoff number of days for a pregnancy for the top 15% of women? (g) **Cutoff for the Bottom 20%:** - What is the cutoff number of days for a pregnancy for the bottom 20% of women? #### Explanation of Approaches: - **Calculating Probabilities for Individuals vs. Samples:** - For individual probabilities (questions a and d), use the standard normal distribution with the given mean and standard deviation. - For sample means (question b), use the standard error to adjust the standard deviation, as the sample size affects variability. - **Interpreting Results:** - Understanding how the probabilities reflect population characteristics helps in statistical reasoning and decision-making. The cutoff points for specific percentiles (questions f and g) indicate how these values distribute across a population. This informs expectations for individual pregnancy durations compared to societal averages.
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