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Chapter 4: Q. 1.18 (page 295)

The manager of the store in the preceding exercise calculated the residual for each point

In the scatterplot and made a dot plot of the residuals. The distribution of residuals is

roughly Normal with a mean of \(0and standard deviation of \)22.92.

a. What percent of the actual sales amounts do you expect to be within $5of their

expected sales amount?

b. The middle 95%of residuals should be between which two values? Use this

information to give an interval of plausible values for the weekly sales revenue if5

linear feet are allocated to the store鈥檚 brand of men鈥檚 grooming products.

Short Answer

Expert verified

(a) Actual sales amount is 17.42%.

(b) Residual is between 卤44.9232and sales between1036.4168-1126.2632

Step by step solution

01

Part (a) Step 1: Given Information

We need to find the percentage of actual sales amount .

02

Part (a) Step 2: Explanation

We are given that:

Mean(渭)=0Standarddeviation(蟽)=22.92x=-5to5

The value of z score is:

z=x-渭蟽=-5-022.92=-0.22z=x-渭蟽=5-022.92=0.22

Now ,

P(-5<x<5)=P(-0.22<z<0.22)P(-5<x<5)=-P(z<-0.22)+P(z<0.22)P(-5<x<5)=0.5871-0.4829P(-5<x<5)=0.1742P(-5<x<5)=17.42%

03

Part (b) Step 1: Given Information

We need to find the residuals and sales.

04

Part (b) Step 2: Explanation

We are given that;

渭=0蟽=22.92middleof95%=(100%-95%)/2=2.5%z=卤1.96andweknowthat,z=x-渭蟽卤1.96=x-5.322.92x=卤44.9232

Now for sales:

x=5y=317.940+152.680脳5y=1081.340weknowthat,y=residual+y^y=卤44.9232+1081.340y=1036.4168y=1126.2632

Hence residual between -$44.9232to$44.9232

And sales between $1036.4168to1126.2632

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