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Suppose the lengths of human pregnancies are normally distributed with u = 266 days and o= 16 days. Complete pafts (a) and (b) below. (a) The figure to the right represents the normal curve with u= 266 days and o = 16 days. The area to the left of X =245 is 0.0947. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) O A. The proportion of human pregnancies that last less than days is O B. The proportion of human pregnancies that last more than days is 245 266 Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) O A. The probability that a randomly selected human pregnancy lasts less than days is O B. The probability that a randomly selected human pregnancy lasts more than days is

Suppose the lengths of human pregnancies are normally distributed with u = 266 days and o= 16 days. Complete pafts (a) and (b) below. (a) The figure to the right represents the normal curve with u= 266 days and o = 16 days. The area to the left of X =245 is 0.0947. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) O A. The proportion of human pregnancies that last less than days is O B. The proportion of human pregnancies that last more than days is 245 266 Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) O A. The probability that a randomly selected human pregnancy lasts less than days is O B. The probability that a randomly selected human pregnancy lasts more than days is

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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## Understanding the Normal Distribution of Human Pregnancies ### Normal Distribution Characteristics - **Mean (µ)**: 266 days - **Standard Deviation (σ)**: 16 days ### Part (a) The graph alongside represents the normal curve with a mean (µ) of 266 days and a standard deviation (σ) of 16 days. It indicates that the area to the left of X = 245 days is 0.0947. #### Problem Interpretation 1. Select an interpretation for the given area. 2. Options: - **Option A**: The proportion of human pregnancies that last less than ___ days is ___. - **Option B**: The proportion of human pregnancies that last more than ___ days is ___. #### Detailed Graph Explanation - The graph is a normal distribution curve centered at 266 days. - A shaded area under the curve to the left of 245 days corresponds to the probability value 0.0947. **Fill in the values as follows:** - **245 days** for specific days - **0.0947** for proportion Thus: - **Option A**: The proportion of human pregnancies that last less than **245** days is **0.0947**. - **Option B**: The proportion of human pregnancies that last more than **245** days is **1 - 0.0947**. ### Part (b) Provide a second interpretation for the same given values. 1. Select the interpretation of the given area. 2. Options: - **Option A**: The probability that a randomly selected human pregnancy lasts less than ___ days is ___. - **Option B**: The probability that a randomly selected human pregnancy lasts more than ___ days is ___. **Fill in the values as follows:** - **245 days** for specific days - **0.0947** for probability Thus: - **Option A**: The probability that a randomly selected human pregnancy lasts less than **245** days is **0.0947**. - **Option B**: The probability that a randomly selected human pregnancy lasts more than **245** days is **1 - 0.0947**.
Transcribed Image Text:## Understanding the Normal Distribution of Human Pregnancies ### Normal Distribution Characteristics - **Mean (µ)**: 266 days - **Standard Deviation (σ)**: 16 days ### Part (a) The graph alongside represents the normal curve with a mean (µ) of 266 days and a standard deviation (σ) of 16 days. It indicates that the area to the left of X = 245 days is 0.0947. #### Problem Interpretation 1. Select an interpretation for the given area. 2. Options: - **Option A**: The proportion of human pregnancies that last less than ___ days is ___. - **Option B**: The proportion of human pregnancies that last more than ___ days is ___. #### Detailed Graph Explanation - The graph is a normal distribution curve centered at 266 days. - A shaded area under the curve to the left of 245 days corresponds to the probability value 0.0947. **Fill in the values as follows:** - **245 days** for specific days - **0.0947** for proportion Thus: - **Option A**: The proportion of human pregnancies that last less than **245** days is **0.0947**. - **Option B**: The proportion of human pregnancies that last more than **245** days is **1 - 0.0947**. ### Part (b) Provide a second interpretation for the same given values. 1. Select the interpretation of the given area. 2. Options: - **Option A**: The probability that a randomly selected human pregnancy lasts less than ___ days is ___. - **Option B**: The probability that a randomly selected human pregnancy lasts more than ___ days is ___. **Fill in the values as follows:** - **245 days** for specific days - **0.0947** for probability Thus: - **Option A**: The probability that a randomly selected human pregnancy lasts less than **245** days is **0.0947**. - **Option B**: The probability that a randomly selected human pregnancy lasts more than **245** days is **1 - 0.0947**.
### Understanding Human Pregnancy Length Using Normal Distribution Suppose the lengths of human pregnancies are normally distributed with a mean (\(\mu\)) of 266 days and a standard deviation (\(\sigma\)) of 16 days. We will explore this distribution through a given problem and related visual representation. #### Problem Scenario Complete parts (a) and (b) below using the provided information. #### Part (b) - Interpretation of the Normal Curve The figure to the right represents a normal curve with \(\mu = 266\) days and \(\sigma = 16\) days. The shaded area between \(x = 290\) and \(x = 305\) is 0.0594. We need to provide two interpretations of this area. ##### Interpretation 1 Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Use ascending order.) 1. **Option A:** - The proportion of human pregnancies that last less than ( ) or more than ( ) days is ( ). 2. **Option B:** - The proportion of human pregnancies that last between ( ) and ( ) days is ( ). ##### Interpretation 2 Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Use ascending order.) 1. **Option A:** - The probability that a randomly selected human pregnancy lasts between ( ) and ( ) days is ( ). 2. **Option B:** - The probability that a randomly selected human pregnancy lasts less than ( ) or more than ( ) days is ( ). #### Graphical Representation The figure shows a bell-shaped normal distribution curve centered at \(x = 266\) days. The two vertical lines highlight the values \(x = 290\) days and \(x = 305\) days on the horizontal axis. The area between these two lines is shaded, illustrating the given probability of 0.0594 (or 5.94%). The curve is symmetrical around the mean, with values spreading out as per the standard deviation. By analyzing this graph along with the provided questions, you can develop a strong understanding of how probabilities and proportions work within the realm of normally distributed data.
Transcribed Image Text:### Understanding Human Pregnancy Length Using Normal Distribution Suppose the lengths of human pregnancies are normally distributed with a mean (\(\mu\)) of 266 days and a standard deviation (\(\sigma\)) of 16 days. We will explore this distribution through a given problem and related visual representation. #### Problem Scenario Complete parts (a) and (b) below using the provided information. #### Part (b) - Interpretation of the Normal Curve The figure to the right represents a normal curve with \(\mu = 266\) days and \(\sigma = 16\) days. The shaded area between \(x = 290\) and \(x = 305\) is 0.0594. We need to provide two interpretations of this area. ##### Interpretation 1 Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Use ascending order.) 1. **Option A:** - The proportion of human pregnancies that last less than ( ) or more than ( ) days is ( ). 2. **Option B:** - The proportion of human pregnancies that last between ( ) and ( ) days is ( ). ##### Interpretation 2 Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Use ascending order.) 1. **Option A:** - The probability that a randomly selected human pregnancy lasts between ( ) and ( ) days is ( ). 2. **Option B:** - The probability that a randomly selected human pregnancy lasts less than ( ) or more than ( ) days is ( ). #### Graphical Representation The figure shows a bell-shaped normal distribution curve centered at \(x = 266\) days. The two vertical lines highlight the values \(x = 290\) days and \(x = 305\) days on the horizontal axis. The area between these two lines is shaded, illustrating the given probability of 0.0594 (or 5.94%). The curve is symmetrical around the mean, with values spreading out as per the standard deviation. By analyzing this graph along with the provided questions, you can develop a strong understanding of how probabilities and proportions work within the realm of normally distributed data.
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