Trystan Horne

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

golfachukc8

Let x = Sales amount.
Given x ~ Normal ($\mu ,\sigma$) where $\mu =\mathrm{}0$ and $\sigma =\mathrm{}22.92$
1) $P\left(\mu -5
$=P\left(\frac{\mu -5-\mu }{\sigma }<\frac{x-\mu }{\sigma }<\frac{\mu +5-\mu }{\sigma }\right)$
$=P\left(\frac{-5}{\sigma } where $z=\frac{x-\mu }{\sigma }$~$N\left(0,1\right)$
$=P\left(\frac{-5}{22.92}
$=P\left(-0.218
$=P\left(z<0.218\right)-P\left(z<-0.218\right)$
$=P\left(z<0.218\right)-1+P\left(z<0.218\right)$
$=2×0.5871-1$ [From Standard Normal Area Table]
$=0.0080$
2) $P\left(-c
$=P\left(\frac{-c-\mu }{\sigma }<\frac{x-\mu }{\sigma }<\frac{c-\mu }{\sigma }\right)$
$=P\left(\frac{-c-\mu }{\sigma }
On comparing with Normal Distribution, $P\left(-1.96

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