The average playing time of compact discs in a large collection is 36 minutes, and the standard deviation is 7 minutes. (a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean? 43 1 standard deviation above the mean 1 standard deviation below the mean 29 2 standard deviations above the mean 2 standard deviations below the mean 50 22 (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 22 and 50 minutes? (Round the answer to the nearest whole number.) At least 75 (c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 15 minutes or greater than 57 minutes? (Round the answer to the nearest

The average playing time of compact discs in a large collection is 36 minutes, and the standard deviation is 7 minutes. (a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean? 43 1 standard deviation above the mean 1 standard deviation below the mean 29 2 standard deviations above the mean 2 standard deviations below the mean 50 22 (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 22 and 50 minutes? (Round the answer to the nearest whole number.) At least 75 (c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 15 minutes or greater than 57 minutes? (Round the answer to the nearest

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The average playing time of compact discs in a large collection is 36 minutes, and the standard deviation is 7 minutes.
(a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
1 standard deviation above the mean
43
1 standard deviation below the mean
29
2 standard deviations above the mean
50
2 standard deviations below the mean
22
(b) Without assuming anything about the distribution of times, at least what percentage of the times are between 22 and 50 minutes? (Round the answer to the nearest whole number.)
At least 75
%
(c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 15 minutes or greater than 57 minutes? (Round the answer to the nearest whole number.)
No more than 11
%
(d) Assuming that the distribution of times is normal, about what percentage of times are between 22 and 50 minutes? (Round the answers to two decimal places, if needed.)
95.45
%
Less than 15 min or greater than 57 min?
0.27
%
Less than 15 min?
0.13
%

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