Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with mean 67 inches and a standard deviation of 2.5". ### Transcription for Educational Website---**Calculation Question:**(h) How much would a baby have to weigh to be among the heaviest 10% of all newborns?- **Given Data:** - Mean weight (\( \mu \)) = 3750 grams - Standard Deviation (SD) (\( \sigma \)) = 550 grams- **Calculation:** - Using a Z-score for the 90th percentile, calculated weight = 3954.855 grams---**Historical Context and Data Analysis:**2. In the mid-19th century, Sir Francis Galton demonstrated, through extensive data collection, that many human characteristics such as height and IQ are distributed throughout the entire population in accordance with the normal distribution. Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with a mean of 67 inches and a standard deviation of 2.5 inches.**Questions:**(a) **Graph this normal distribution and label the x-axis.**- **Explanation:** - A normal distribution graph is symmetrical with a bell curve shape centered around the mean (67 inches in this case). The x-axis would be labeled with height in inches, typically ranging several standard deviations above and below the mean (e.g., from 60 to 74 inches in increments).(b) **What proportion of these men were between 66 and 68 inches tall?**- **Explanation:** - Using the properties of the normal distribution, calculate the Z-scores for 66 and 68 inches. Determine the proportion of the area under the curve between these Z-scores to find the percentage of men in this height range.---**Note:** For part (b), specific statistical techniques such as the use of Z-tables or probability calculations will provide a more precise answer.

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Answered: 2.In the mid-19thcentury, Sir Francis…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with mean 67 inches and a standard deviation of 2.5".

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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