A manufacturer has developed a specialized metal alloy for use in jet engines. In its pure form, the alloy starts to soften at 1500 F. Hoever, small amounts of impurities in production cause the actual temperature at hich the alloy starts to lose strength to vary around that mean, in a !aussian distri"ution ith standard deviation # 10.5 degrees F. If the manufacturer ants to ensure that no more than 1 in 10,000 of its commercial products ill suffer from softening, hat should it set as the ma$imum temperature to hich the alloy can "e e$posed% Hint& 'efer to the ($cel )orm*Functions *preadsheet. ($cel )orm* Functions *preadsheet.$ls$ 1+0.-50 F
r
A carefully machined ire comes off an assem"ly line ithin a certain tolerance. Its target diameter is 100 microns, and the ires produced have a uniform distri"ution of diameters, "eteen /11 microns and - microns from the target. 2hat is the mean and standard deviation of the uniform distri"ution of ire diameters% Hint& 3se the 46 and ($cel 'and78 *preadsheet. 46 and ($cel 'and.$ls$ A 3niform 9istri"ution ith mean # 10- microns and standard deviation # .:0; microns. $ A 3niform 9istri"ution ith mean # 10- microns and standard deviation # 11.5+ microns. $ A !aussian distri"ution that, in
A population of people suffering from 6achycardia 7occasional rapid heart rate8, agrees to test a ne medicine that is supposed to loer heart rate. In the population "eing studied, "efore ta>ing any medicine the mean heart rate as 10 "eats per minute, ith standard deviation # 15 "eats per minute. After "eing given the medicine, a sample of +5 people had an average heart rate of 11 "eats per minute. 2hat is the pro"a"ility that this much variation from the mean could have occurred "y chance alone% Hint& 3se the 6ypical
6o stoc>s have the folloing e$pected annual returns& il stoc>
�
e$pected return # -@ ith standard deviation # 1@
I6 stoc>
�
e$pected return # 1+@ ith standard deviation # 5@
6he *toc>s prices have a small negative correlation& ' # /.. 2hat is the 4ovariance of the to stoc>s% Hint& 3se the Alge"ra ith !aussians *preadsheet. Alge"ra ith !aussians.$ls$ /.001$ /.0: $ /.00;15 r
6o stoc>s have the folloing e$pected annual returns& il stoc> I6 stoc>
�
�
e$pected return # -@ ith standard deviation # 1@ e$pected return # 1+@ ith standard deviation # 5@
6he *toc>s prices have a small negative correlation& ' # /.. Assume return data for the to stoc>s is standardized so that each is represented as having mean 0 and standard deviation 1. il is plotted against I6 on the 7$,y8 a$is. 2hat is the covariance% Hint& 3se the *tandardization *preadsheet. *tandardization *preadsheet.$ls$ /.
r
6o stoc>s have the folloing e$pected annual returns& il stoc> I6 stoc>
�
�
e$pected return # -@ ith standard deviation # 1@ e$pected return # 1+@ ith standard deviation # 5@
6he *toc>s prices have a small negative correlation& ' # /.. 2hat is the standard deviation of a portfolio consisting of ;0@ il and 0@ I6% Hint& 3se either the Alge"ra ith !aussians or the =ar>oitz oitz
$ $ $
10.++@
r
6o stoc>s have the folloing e$pected annual returns& il stoc> I6 stoc>
�
�
e$pected return # -@ ith standard deviation # 1@ e$pected return # 1+@ ith standard deviation # 5@
6he *toc>s prices have a small negative correlation& ' # /.. 3se =* *olver and the =ar>oitz s ith loest volatility. *olver Add/In.$ls$ =ar>oitz
$ r
Bou are a data/analyst for a restaurant chain and are as>ed to forecast first/year revenues from ne store locations. Bou use census tract data to develop a linear model. Bour first model has a standard deviation of model error of C5,000 at a correlation of ' # .0. Bour "oss as>s you to >eep or>ing on improving the model until the ne standard deviation of model error is C15,000 or less. 2hat positive correlation ' ould you need to have a model error of C15,000% 7)ote& you can anser this Duestion "y ma>ing small additions to the 4orrelation and =odel (rror spreadsheet8. 4orrelation and =odel (rror.$ls$ ' # .+: ' # .:00
$ r
An automo"ile parts manufacturer uses a linear regression model to forecast the dollar value of the ne$t years� orders from current customers as a function of a eighted sum of their past/years� orders. 6he model error is assumed !aussian ith standard deviation of C10,000. If the correlation is ' # ., and the point forecast orders C5.1 million, hat is the pro"a"ility that the customer ill order more than C5. million% Hint& 3se the 6ypical
$ r
An automo"ile parts manufacturer uses a linear regression model to forecast the dollar value of the ne$t years� orders from current customers as a function of a eighted sum of that customer� s past/years orders. 6he linear correlation is ' # . . After standardizing the $ and y data, hat portion of the uncertainty a"out a customer� s order size is eliminated "y their historical data com"ined ith the model% Hint& 3se the 4orrelation and <.I.!. *preadsheet. 4orrelation and <.I.!..$ls$ +.@
r
4ustomers ho use online chat support can rate the help they receive from a customer support or>er as a 0 7useless8, a 1, , , +, or 5 7e$cellent8. 6he mean rating is .-5, ith standard deviation # 1.01. A ne support or>er named Ear"ara has received, over her first 100 chat sessions, an average rating of .;. Her "oss calls her in and threatens to fire her if her performance does not improve. Ear"ara replies � Its just "ad luc> / I� ve had more than my share of unhappy customers today.� 2ho is most li>ely right% Hint& 3se the 6ypical
r
Bour company currently has no ay to predict ho long visitors ill spend on the 4ompany�s e" site. All it >non is the average time spent is 55 seconds, ith an appro$imately !aussian distri"ution and standard deviation of - seconds. It ould "e possi"le, after investing some time and money in analytics tools, to gather and analyzing information a"out visitors and "uild a linear predictive model ith a standard deviation of model error of + seconds. Ho much ould the <.I. !. of that model "e% Hint& 3se the 4orrelation and <.I.!. *preadsheet Ho to use the A34 calculator.pdf 5.@ +:.@ 1.5@
$ $ $
An automo"ile parts manufacturer uses a linear regression model to forecast the dollar value of the ne$t years� orders from current customers as a function of a eighted sum of their past/years� orders. 6he model error is assumed !aussian ith standard deviation of C10,000. 6o the nearest dollar, hat is the range a"ove and "elo each ing small modifications to the 4orrelation and =odel (rror *preadsheet. 4orrelation and =odel (rror.$ls$ 6he -0@ confidence interval is from C:,:1 "elo to C:,:1 a"ove the
A restaurant offers different dinner � specials� each ee>night. 6he mean cash register receipt per ta"le on 2ednesdays is C;5.5 ith standard deviation of C1.50. 6he restaurant e$periments one 2ednesday ith changing the � special � from "lue fish to lo"ster. 6he average amount spent "y :5 customers is C;;.0. Ho pro"a"le is it that 2ednesday receipts are "etter than average "y chance alone% Hint& 3se the 6ypical
$ r
A 3niversity admissions test has a !aussian distri"ution of test scores ith a mean of 500 and standard deviation of 100. ne student out/performed -;.+@ of all test ta>ers. 2hat as their test score 7rounded to the nearest hole num"er8% Hint& 'efer to the ($cel )orm*Functions *preadsheet.
($cel )orm* Functions *preadsheet.$ls$ -; 0
$ $
. Bour company currently has no ay to predict ho long visitors ill spend on the 4ompany�s e" site. All it >non is the average time spent is 55 seconds, ith an appro$imately !aussian distri"ution and standard deviation of - seconds. It ould "e possi"le, after investing some time and money in analytics tools, to gather and analyzing information a"out visitors and "uild a linear predictive model ith a standard deviation of model error of + seconds. Ho much ould the <.I. !. of that model "e% Hint& 3se the 4orrelation and <.I.!. *preadsheet Ho to use the A34 calculator.pdf 5;.@
r
