Answered: Find the area of the shaded region.

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

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

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A graph with a bell-shaped curve, divided into 2 regions by a vertical line. The vertical line extends from the bell curve to the x-axis, and is located on the left half, under the curve. The region on the left of this line is shaded. The x-axis below the vertical line is labeled 75.

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate 83, which is to the left of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded.

3. Assume that military aircraft use ejection seats designed for men weighing between 145.4 lb and 203 lb. If women's weights are normally distributed with a mean of 178.5 lb and a standard deviation of 49.4lb, what percentage of women have weights that are within those limits? Are many women excluded with those specifications?

4. Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of 0.63°F.

a. A hospital uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate?

b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result ispositive, but the subject is not really sick.)

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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