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

Question

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

golfachukc8 · Accepted Answer

Let x = Sales amount.  Given x ~ Normal (μ,σ) where μ=$0 and σ=$22.92  1) P(μ−5&amp;lt;x&amp;lt;μ+5)  =P(μ−5−μσ&amp;lt;x−μσ&amp;lt;μ+5−μσ)  =P(−5σ&amp;lt;z&amp;lt;5σ) where z=x−μσ~N(0,1)  =P(−522.92&amp;lt;z&amp;lt;522.92)  =P(−0.218&amp;lt;z&amp;lt;0.218)  =P(z&amp;lt;0.218)−P(z&amp;lt;−0.218)  =P(z&amp;lt;0.218)−1+P(z&amp;lt;0.218)  =2×0.5871−1 [From Standard Normal Area Table]  =0.0080  2) P(−c&amp;lt;x&amp;lt;c)=0.95  =P(−c−μσ&amp;lt;x−μσ&amp;lt;c−μσ)  =P(−c−μσ&amp;lt;z&amp;lt;c−μσ)  On comparing with Normal Distribution, P(−1.96&amp;lt;z&amp;lt;1.96)=0.95  ∴−c−μσ=−1.96           c−μσ=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

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

Answered question

Answer & Explanation

New Questions in High school statistics