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13.36 (EX) Pregnancy lengths 2/2: What is the probability that the average pregnancy length exceeds 270 days? P(X>270)=P(Z > |) = . (Round the 1st number to 1 decimal and the 2nd number to 4 decimals)

13.36 (EX) Pregnancy lengths 2/2: What is the probability that the average pregnancy length exceeds 270 days? P(X>270)=P(Z > |) = . (Round the 1st number to 1 decimal and the 2nd number to 4 decimals)

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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**Educational Text: Probability and Pregnancy Lengths** Title: 13.36 (EX) Pregnancy Lengths 2/2 **Question:** What is the probability that the average pregnancy length exceeds 270 days? **Mathematical Expression:** \( P(\bar{X} > 270) = P(Z > \_\_) = \_\_ \) **Instructions:** - Round the first number to 1 decimal place. - Round the second number to 4 decimal places. **Analysis:** This question pertains to the concept of probability in statistics, specifically related to the normal distribution of pregnancy lengths. The goal is to calculate the probability that the mean (average) pregnancy length exceeds 270 days. To address this problem, we need to utilize the standard normal distribution, represented here as \( Z \). The process involves: 1. Calculating the Z-score, which standardizes the average pregnancy length to a scale that measures how many standard deviations an element is from the mean. 2. Finding the probability associated with the calculated Z-score using the standard normal distribution table or a computational tool. By understanding and applying these calculations, one can determine the likelihood of a pregnancy lasting longer than 270 days.
Transcribed Image Text:**Educational Text: Probability and Pregnancy Lengths** Title: 13.36 (EX) Pregnancy Lengths 2/2 **Question:** What is the probability that the average pregnancy length exceeds 270 days? **Mathematical Expression:** \( P(\bar{X} > 270) = P(Z > \_\_) = \_\_ \) **Instructions:** - Round the first number to 1 decimal place. - Round the second number to 4 decimal places. **Analysis:** This question pertains to the concept of probability in statistics, specifically related to the normal distribution of pregnancy lengths. The goal is to calculate the probability that the mean (average) pregnancy length exceeds 270 days. To address this problem, we need to utilize the standard normal distribution, represented here as \( Z \). The process involves: 1. Calculating the Z-score, which standardizes the average pregnancy length to a scale that measures how many standard deviations an element is from the mean. 2. Finding the probability associated with the calculated Z-score using the standard normal distribution table or a computational tool. By understanding and applying these calculations, one can determine the likelihood of a pregnancy lasting longer than 270 days.
**13.36 (EX) Pregnancy Lengths 1/2** The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. A study enrolls a random sample of 16 pregnant women. - The mean of the sampling distribution of \( \bar{X} \) is **266**. (No decimal) - The standard deviation of the sampling distribution of \( \bar{X} \) is **4**. (No decimal)
Transcribed Image Text:**13.36 (EX) Pregnancy Lengths 1/2** The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. A study enrolls a random sample of 16 pregnant women. - The mean of the sampling distribution of \( \bar{X} \) is **266**. (No decimal) - The standard deviation of the sampling distribution of \( \bar{X} \) is **4**. (No decimal)
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