Answered: The heights of a three-year-old female…

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

The heights of a three-year-old female patients are approximately normal with mean = 38.72 inches and standard deviation = 3.17 inches. Find the probability that randomly selected girl is between 34 and 42 inches tall, inclusive P(34 less than or equal to x less than or equal to 42).

A. Draw a normal curve with parameters labeled.

B. Use a graphing calculator to find the probability with x1 = 34, x2 = 42, mean = 38.72, and standard deviation = 3.17.

C. Standardize the normal distribution and find z1, z2. Then find the probability with z1, z2, mean = 0, and standard deviation = 1 using a graphing calculator.

D. Find the heights of girls corresponding to 68% of data and shaded the region on the curve.

E. Which height is corresponding to 90th percentile.

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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