anonymous
  • anonymous
Find the area under the normal distribution curve between z = 1.30 and z = 3.25.
Mathematics
chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
which option do you want to use: table or calculator?
anonymous
  • anonymous
table
jim_thompson5910
  • jim_thompson5910
ok we can use a table like this one https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

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jim_thompson5910
  • jim_thompson5910
does something like that look familiar?
anonymous
  • anonymous
Yes Thanks I'm kind of confused with this lesson
jim_thompson5910
  • jim_thompson5910
first we'll find P(Z < 1.30) look at the row that starts with `1.3` then find the column that has `.00` at the top of the column what number is at the intersection of that row and column?
anonymous
  • anonymous
.90320
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
do the same for P(Z < 3.25)
jim_thompson5910
  • jim_thompson5910
look at the row starting with `3.2` and the column starting with `0.05`
anonymous
  • anonymous
.99942
jim_thompson5910
  • jim_thompson5910
now subtract the two (bigger - smaller)
anonymous
  • anonymous
wow Thanks a lot. That's an answer choice I appreciate it
jim_thompson5910
  • jim_thompson5910
you should get .99942-.90320 = 0.09622 so P(1.30 < z < 3.25) = 0.09622 The rule I used was \[\Large P({\color{red}{a}} < z < {\color{blue}{b}}) = P(z < {\color{blue}{b}}) - P(z < {\color{red}{a}})\] where b > a so, \[\Large P({\color{red}{1.30}} < z < {\color{blue}{3.25}}) = P(z < {\color{blue}{3.25}}) - P(z < {\color{red}{1.30}})\]

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