Solution Stat 328 Quiz Summer 2000
1. (a) C œ "'Þ&, = œ *Þ($
(b) There is an (inadvertent) twist in this problem. It has to do with the fact that we are dealing with
temperature DIFFERENCES. Note that
ÐMay31>/7:G • May1>/7:GÑ œ aÐÞ&&&'ÐMay31>/7:J Ñ • "(Þ((()Ñ • ÐÞ&&&'ÐMay1>/7:J Ñ • "(Þ((()Ñb
That is
ÐMay31>/7:G • May1>/7:GÑ œ Þ&&&'aMay31>/7:J • May1>/7:J b
and the whole " • "(Þ((()" business washes out of the problem. The fact is that if a "C" data set has
mean C and standard deviation =C
and we make data values A from the C 's via
A œ +C € ,
then the "A" data set has
mean A œ +C € , and standard deviation =A œ k+k=C
So
Centigrade mean œ ÐÞ&&&'ÑÐ"'Þ&Ñ œ *Þ"' and Centigrade standard deviation œ ÐÞ&&&'ÑÐ*Þ($Ñ œ &Þ%"
(c) "'Þ& „ #Þ&(" *Þ($
È'
(d) "'Þ& „ #Þ&("Ð*Þ($ÑÉ" €
"
'
(e) D œ !•"&
"" œ • "Þ$' so the desired probability is Þ& • Þ%"$" œ Þ!)'*. There is about a 9% chance of
this kind of occurrence.
2. (a) UÐÞ#&Ñ œ $rd ordered data value œ ()
(b) The histogram is surely not bell-shaped. It is instead long-tailed (or skewed) right.
(c) The confidence level associated with Ð=7+66/=> C3 ß 6+<1/=> C3 Ñ as a prediction interval for one more C
#
is " • "!€"
œ Þ)"). I'm "82% sure" the next price will be in the range $(&ß !!! to $$'!ß !!!.