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Chapter 6: Q. 6.23 (page 260)

Sketch the normal distribution with

(a)渭=3;蟽=3(b)渭=1;蟽=3(c)渭=3;蟽=1

Short Answer

Expert verified

(a) The normal distribution with 渭=3;蟽=3is:

(b) The normal distribution with 渭=1;蟽=3is:

(c) The normal distribution with role="math" localid="1652507031330" 渭=3;蟽=1is:

Step by step solution

01

Part (a) Step 1. Given Information.

渭=3;蟽=3

02

Part (a) Step 2. Sketch the normal distribution.

The normal distribution is:

03

Part (b) Step 1. Sketch the normal distribution.

The normal distribution with 渭=1;蟽=3is:

04

Part (b) Step 1. Sketch the normal distribution.

The normal istribution with 渭=3;蟽=1is:

05

Part (c) Step 2. Sketch all three distributions.

Sketch all the distribution in a single graph:

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Most popular questions from this chapter

Determinez0.33

A variable is normally distributed with mean 10 and standard deviation 3.

a. Determine and interpret the quartiles of the variable.

b. Obtain and interpret the seventh decile.

c. Find the value that 35% of all possible values of the variable exceed.

d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.99 and two outside areas of 0.005. Interpret your answer.

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?

A variable is normally distributed with mean 10and standard deviation 3.

Part (a): Determine and interpret the quartiles of the variable.

Part (b): Obtain and interpret the seventh percentile.

Part (c): Find the value that 35%of all possible values of the variable exceed.

Part (d): Find the two values that divide the area under the corresponding normal curve into a middle area of 0.99and two outside areas of 0.005. Interpret your answer.

Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?
See all solutions

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