Answered: A population of values has a normal…

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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A population of values has a normal distribution with μ=154.6 and σ=33.9 You intend to draw a random sample of size n=86.

Find the probability that a single randomly selected value is less than 145.5.
P(X < 145.5) = Round to 4 decimal places.
Find the probability that the sample mean is less than 145.5.
P(¯¯¯XX¯ < 145.5) = Round to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 228.1-cm and a standard deviation of 1.2-cm. For shipment, 16 steel rods are bundled together.

Find the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 227.1-cm.

P(¯¯¯XX¯ > 227.1-cm) =

Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

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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