13.11 Random numbers. If you ask a computer to generate “random numbers" between 0and 5, you will get observations from a uniform distribution. Figure 13.12 shows the densitycurve for a uniform distribution. This curve takes the constant value 0.2 between 0 and 5 andis zero outside that range. Use this density curve to answer these questions.a. Why is the total area under the curve equal to 1?b. The curve is symmetric. What is the value of the mean and median?c. What percentage of the observations lie between 4 and 5?d. What percentage of the observations lie between 1.5 and 3?height = 0,20Moore/Notz, Statistics: Concepts and Controversies, 10e, 0 2020 W. H. Freeman and CompanyFigure 13.12 The density curve of a uniform distribution, for Exercise 13.11.Observations from this distribution are spread "at random" between 0 and 5. IQ test scores. Figure 13.13 is a stemplot of the IQ scores that are consistent with the 2018article "Flynn effect and its reversal are both environmentally caused." This distribution isvery close to Normal with mean 100 and standard deviation 10. Use the Normal distributionwith mean 100 and standard deviation 10 as a description of the IQ test scores of all adults.Use this distribution and the 68-95-99.7 rule to answer Exercises 13.12 to 13.14.8 | 2467789999 0001222455555667788888899900000111112234410105555566677888991102233115566812234Moore/Notz, Statistics: Concepts andControversies, 10e, © 2020 W. H.Freeman and CompanyFigure 13.13 Stemplot of the IQ scores of 80 adults, forExercises 13.12 to 13.14. (Key: A stem of 8 and a leaf of 2means 82.)13.12 Between what values do the IQ scores of 68% of all adults lie?

X ~ uniform(a,b) f(x) = 1b-a; a ≤x≤b

13.11 Random numbers. If you ask a computer to generate “random numbers" between 0 and 5, you will get observations from a uniform distribution. Figure 13.12 shows the density curve for a uniform distribution. This curve takes the constant value 0.2 between 0 and 5 and is zero outside that range. Use this density curve to answer these questions. a. Why is the total area under the curve equal to 1? b. The curve is symmetric. What is the value of the mean and median? c. What percentage of the observations lie between 4 and 5? d. What percentage of the observations lie between 1.5 and 3? -height = 0.20

13.11 Random numbers. If you ask a computer to generate “random numbers" between 0 and 5, you will get observations from a uniform distribution. Figure 13.12 shows the density curve for a uniform distribution. This curve takes the constant value 0.2 between 0 and 5 and is zero outside that range. Use this density curve to answer these questions. a. Why is the total area under the curve equal to 1? b. The curve is symmetric. What is the value of the mean and median? c. What percentage of the observations lie between 4 and 5? d. What percentage of the observations lie between 1.5 and 3? -height = 0.20

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

13.11 Random numbers. If you ask a computer to generate “random numbers" between 0
and 5, you will get observations from a uniform distribution. Figure 13.12 shows the density
curve for a uniform distribution. This curve takes the constant value 0.2 between 0 and 5 and
is zero outside that range. Use this density curve to answer these questions.
a. Why is the total area under the curve equal to 1?
b. The curve is symmetric. What is the value of the mean and median?
c. What percentage of the observations lie between 4 and 5?
d. What percentage of the observations lie between 1.5 and 3?
height = 0,20
Moore/Notz, Statistics: Concepts and Controversies, 10e, 0 2020 W. H. Freeman and Company
Figure 13.12 The density curve of a uniform distribution, for Exercise 13.11.
Observations from this distribution are spread "at random" between 0 and 5.

IQ test scores. Figure 13.13 is a stemplot of the IQ scores that are consistent with the 2018
article "Flynn effect and its reversal are both environmentally caused." This distribution is
very close to Normal with mean 100 and standard deviation 10. Use the Normal distribution
with mean 100 and standard deviation 10 as a description of the IQ test scores of all adults.
Use this distribution and the 68-95-99.7 rule to answer Exercises 13.12 to 13.14.
8 | 24
6778999
9 00012224
555556677888888999
000001111122344
10
10
555556667788899
11
02233
11
55668
12
234
Moore/Notz, Statistics: Concepts and
Controversies, 10e, © 2020 W. H.
Freeman and Company
Figure 13.13 Stemplot of the IQ scores of 80 adults, for
Exercises 13.12 to 13.14. (Key: A stem of 8 and a leaf of 2
means 82.)
13.12 Between what values do the IQ scores of 68% of all adults lie?

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