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Chapter 6: Q.6.118 (page 283)

Explain in detail what a normal probability plot is and how it is used to assess the normality of a variable.

Short Answer

Expert verified

The data is spread in a linear way.

Step by step solution

01

Given Information

Consider the concept of "variable normalcy."

A random variable's normality is a quality of a normal distribution-distributed random variable.

02

Explanation

The normalcy probability plot is a graphical method for determining whether or not data is normally distributed. The line is constructed between observed variable values and normal scores. If the variable is regularly distributed, the plot should be linearly approximated; otherwise, it should not be.

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Most popular questions from this chapter

Dispensing Coffee. A coffee machine is supposed to dispense 6 fluid ounces (fi oz) of coffee into a paper cup. In reality, the amounts dispensed vary from cup to cup. In fact, the amount dispensed. in fi oz. is a variable with density curve y=2 for 5.75< x < 6.25, and y = 0 otherwise.

a. Graph the density curve of this variable.

b. Show that the area under this density curve to the left of any number x between 5.75 and 6 .25 equals 2x-11.5. What percentage of cups dispensed by this machine contain

c. less than 6 fi oz?

d. between 5.9 and 6.1 11 oz

e. at least 5.8 fi oz.?

A variable is normally distributed with a mean 10 and standard deviation3. Find the percentage of all possible values of the variable that

a. lie between 6and 7.

b. are at least 10 .

c. are at most 17.5 .

Find the following z-scores.

a. Z0.03

b.z0.005

11. Answer true or false to each statement. Explain your answers.

a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.

b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

6.31 Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y=1/30for 0<x<30, and y=0 otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number xbetween 0 and 30 equals x/30.

What percentage of the time does John wait for the train
c. less than 5 minutes?
d. between 10 and 15 minutes?
e. at least 20 minutes?
See all solutions

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