Answered: Furnace repair bills are normally…

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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If we were to define an event as being unusual if it occurs less than 5% of the time, would we consider a sample of size n=36 that had a sample mean of 87kg to be considered unusual? Why or why not?

Furnace repair bills are normally distributed with a mean of µ = 273 dollars and a standard deviation of σ = 25 dollars. If n = 100 of these repair bills are randomly selected, find the probability that they have a mean cost, , between 270 dollars and 276 dollars. i.e. find P(270 < < 276). In calculating the z-score, round your z-score to two decimal places. Use the normal table to find the probability and give answer to 4 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.

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If we were to define an event as being unusual if it occurs less than 5% of the time, would we consider a sample of size n=36 that had a sample mean of 87kg to be considered unusual? Why or why not? (hint: number 6 gives the 95th percentile).

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