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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

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.

As reported in Runner's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61minutes and standard deviation 9 minutes.

Part (a): Determine the percentage of finishers who have times between 50and 70minutes.

Part (b): Determine the percentage of finishers who have times less than 75minutes.

Part (c): Obtain and interpret the 40th percentile for the finishing times.

Part (d): Find and interpret the 8th decile for the finishing times.

For the standard normal curve, find the z- score(s)

a. that has area 0.30 to its left.

b. that has area 0.10 to its right.

c. z0.025,z0.05,z0.01andz0.005.

d. that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas

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

Use Table II to obtain the areas under the standard normal curve required in Exercises 6.59-6.66. Sketch a standard normal curve and shade the area of interest in each problem.

6.60 Determine the area under the standard normal curve that lies to the left of

a. -0.87.

b.3.56

c. 5.12.
See all solutions

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