Answered: Let x be a continuous random variable…

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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Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 26. Find the value of x so that the area under the normal curve to the left of x is approximately 0.9924.

Round your answer to two decimal places.

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.

Expert Solution

Step 1

The z score can be calculated as:

$z = \frac{x - μ}{σ}$

The required z score that is associated with the area under the normal curve to the left of x is approximately 0.9924 can be obtained by using the standard normal table. The value of z at p = 0.9924 is 2.43.

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