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

Trystan Horne

Trystan Horne

Answered question

2022-02-12

The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
A. What percent of the actual sales amount do you expect to be within $5 of 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 if 5 linear feet are allocated to the stores

Answer & Explanation

golfachukc8

golfachukc8

Beginner2022-02-13Added 13 answers

Let x = Sales amount.
Given x ~ Normal (μ,σ) where μ=$0 and σ=$22.92
1) P(μ5<x<μ+5)
=P(μ5μσ<xμσ<μ+5μσ)
=P(5σ<z<5σ) where z=xμσ~N(0,1)
=P(522.92<z<522.92)
=P(0.218<z<0.218)
=P(z<0.218)P(z<0.218)
=P(z<0.218)1+P(z<0.218)
=2×0.58711 [From Standard Normal Area Table]
=0.0080
2) P(c<x<c)=0.95
=P(cμσ<xμσ<cμσ)
=P(cμσ<z<cμσ)
On comparing with Normal Distribution, P(1.96<z<1.96)=0.95
cμσ=1.96           cμσ=1.96
c+μσ=1.96            c=1.96×6)+μ
c=(1.96×22.92)0            c=(1.96×22.92)+0
c=44.922            c=44.922

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