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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates​ fuse, growth​ stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.7 years and a standard deviation of 16.1 months.   ​(a) What is the probability a​ male's growth plates fuse after age  21​? ​(Round to four decimal places as​ needed.)

The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates​ fuse, growth​ stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.7 years and a standard deviation of 16.1 months.   ​(a) What is the probability a​ male's growth plates fuse after age  21​? ​(Round to four decimal places as​ needed.)

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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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates​ fuse, growth​ stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.7 years and a standard deviation of 16.1 months.
 
​(a) What is the probability a​ male's growth plates fuse after age 
21​?
​(Round to four decimal places as​ needed.)
**Standard Normal Distribution Table** This page demonstrates a standard normal distribution table, used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution scale. **Diagram Explanation:** The top of the page features a bell-shaped curve representing the standard normal distribution. This is a symmetric curve centered around a mean (μ) of zero with a standard deviation (σ) of one. A shaded area under the curve is labeled as "Area," which correlates with a particular value of "z" on the table below. **Table Explanation:** The table is structured to identify z-scores along with their corresponding cumulative probabilities. It is used to determine the probability of a standard normal random variable being less than or equal to a certain value. - **Column "z":** This column provides z-scores ranging from -3.4 to 0.0. The z-score represents the number of standard deviations a data point is from the mean. - **Columns 0.00 - 0.09:** Each row in these columns represents a specific z-score value, calculated by the combination of the z value from the row and the column heading. For example, a z-score of -2.57 can be found in the row -2.5, column 0.07. - **Values in the Table:** Each cell value represents the cumulative probability that a standard normal random variable is less than or equal to the z-score. For example, for a z-score of -2.57, the table provides a cumulative probability of approximately 0.0051. This table aids in statistical calculations for hypothesis testing and confidence interval estimation, offering critical insights for researchers and students alike.
Transcribed Image Text:**Standard Normal Distribution Table** This page demonstrates a standard normal distribution table, used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution scale. **Diagram Explanation:** The top of the page features a bell-shaped curve representing the standard normal distribution. This is a symmetric curve centered around a mean (μ) of zero with a standard deviation (σ) of one. A shaded area under the curve is labeled as "Area," which correlates with a particular value of "z" on the table below. **Table Explanation:** The table is structured to identify z-scores along with their corresponding cumulative probabilities. It is used to determine the probability of a standard normal random variable being less than or equal to a certain value. - **Column "z":** This column provides z-scores ranging from -3.4 to 0.0. The z-score represents the number of standard deviations a data point is from the mean. - **Columns 0.00 - 0.09:** Each row in these columns represents a specific z-score value, calculated by the combination of the z value from the row and the column heading. For example, a z-score of -2.57 can be found in the row -2.5, column 0.07. - **Values in the Table:** Each cell value represents the cumulative probability that a standard normal random variable is less than or equal to the z-score. For example, for a z-score of -2.57, the table provides a cumulative probability of approximately 0.0051. This table aids in statistical calculations for hypothesis testing and confidence interval estimation, offering critical insights for researchers and students alike.
**Standard Normal Distribution Table (Page 2)** *Diagram Description:* At the top left, there is a graph of a bell-shaped curve representing the standard normal distribution. This curve is symmetric and centered at zero. An arrow labeled "Area" points to the left of a position on the x-axis marked as "z," indicating the cumulative probability from the extreme left up to the chosen z-value. *Table Description:* Below the diagram is Table V, a continuation of the Standard Normal Distribution Table. This table provides cumulative probability values for the standard normal distribution, often used in statistics to determine the probability that a statistic is observed below, above, or between values on a bell curve. The z-scores are listed vertically on the leftmost column, ranging from 0.0 to 3.4. The top row, with columns labeled from 0.00 to 0.09, represents the hundredths place, providing precise probability values. *Example Interpretation:* For a z-score of 1.5 and a hundredths value of 0.06 (located in the column under 0.06), the cumulative probability is 0.9332. This means that approximately 93.32% of the data under a standard normal distribution falls below a z-score of 1.56. This table is an essential tool in statistics for determining probabilities and critical values involved in hypothesis testing and confidence interval estimation.
Transcribed Image Text:**Standard Normal Distribution Table (Page 2)** *Diagram Description:* At the top left, there is a graph of a bell-shaped curve representing the standard normal distribution. This curve is symmetric and centered at zero. An arrow labeled "Area" points to the left of a position on the x-axis marked as "z," indicating the cumulative probability from the extreme left up to the chosen z-value. *Table Description:* Below the diagram is Table V, a continuation of the Standard Normal Distribution Table. This table provides cumulative probability values for the standard normal distribution, often used in statistics to determine the probability that a statistic is observed below, above, or between values on a bell curve. The z-scores are listed vertically on the leftmost column, ranging from 0.0 to 3.4. The top row, with columns labeled from 0.00 to 0.09, represents the hundredths place, providing precise probability values. *Example Interpretation:* For a z-score of 1.5 and a hundredths value of 0.06 (located in the column under 0.06), the cumulative probability is 0.9332. This means that approximately 93.32% of the data under a standard normal distribution falls below a z-score of 1.56. This table is an essential tool in statistics for determining probabilities and critical values involved in hypothesis testing and confidence interval estimation.
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