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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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