anonymous
  • anonymous
Statistics The diameters of grapefruits in a certain orchard are normally distributed with a mean of 7.30 inches and a standard deviation of 0.80 inches. Show all work. (A) What percentage of the grapefruits in this orchard have diameters less than 6.7 inches? (B) What percentage of the grapefruits in this orchard are larger than 7.20 inches? What I have wrote out mean=m=7.30 Standard deviation=s=0.80 (A) what % have diameters less than 6.7 (B) what %are larger than 7.20
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
A is asking: P(X<6.7)
amistre64
  • amistre64
B is asking P(X>7.2)
amistre64
  • amistre64
z = (6.7 - mean)/sd

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anonymous
  • anonymous
6.7-7.30/0.80
amistre64
  • amistre64
good, thats our z score for A
amistre64
  • amistre64
we get a negative and we know that it wants the value of everything to the left of it
amistre64
  • amistre64
.5 - zvalue
amistre64
  • amistre64
zvalue will probably be called a Pvalue later in the book
anonymous
  • anonymous
-0.75
amistre64
  • amistre64
yep
anonymous
  • anonymous
Can we use the bell curve ?
amistre64
  • amistre64
we are .
anonymous
  • anonymous
yes, mathtalk that is what they are all made of (im in statistics-the book says elementary statistics- my first class of it0
anonymous
  • anonymous
somebody show how to proceed here
anonymous
  • anonymous
please
anonymous
  • anonymous
so 0.5000-0.2734(from the table)=
amistre64
  • amistre64
its alot to wrap up form previous posts ... but in a nutshell, you get a zscore and look that up in a table to get a value
amistre64
  • amistre64
then work it into the question to find an answer
amistre64
  • amistre64
.2734 is good, so that should do it for A
amistre64
  • amistre64
B is trickier in that it wants values all to the right of z
amistre64
  • amistre64
same concept, but we have to adjust our thinking a little to accomodate for it
anonymous
  • anonymous
don't we do 0.5000-0.2734?
amistre64
  • amistre64
yes
amistre64
  • amistre64
A is the result of .5 - .2734
anonymous
  • anonymous
for the first one? right.
amistre64
  • amistre64
yep
anonymous
  • anonymous
oh ok, then i have 0.2266
amistre64
  • amistre64
good
anonymous
  • anonymous
so then I write it like this right? P(x<6.7)=0.23
amistre64
  • amistre64
B needs some care taken to it.|dw:1320180861380:dw|
amistre64
  • amistre64
A asks for a % so we gotta rewrite .2266 as 22.66%
anonymous
  • anonymous
*100 .2266*100=22.66%
amistre64
  • amistre64
that looks good to me
anonymous
  • anonymous
ok, on to the second one!
anonymous
  • anonymous
are you still here?
amistre64
  • amistre64
im here
amistre64
  • amistre64
lets figure the z score to get started
anonymous
  • anonymous
ok, I have been having loading problems, so I thought it was me.
anonymous
  • anonymous
ok
anonymous
  • anonymous
P(x>7.2)
anonymous
  • anonymous
wait I am trying to figure it.
amistre64
  • amistre64
z = (7.2-7.3)/.8 .... same process, different numbers
anonymous
  • anonymous
x-mean/stan dev. 7.20-7.30/0.80
anonymous
  • anonymous
-01/0.80 -0.125/0.80 -0.15625
amistre64
  • amistre64
got some typos in there... but your on the right track -.1/.8 = -.125
amistre64
  • amistre64
7.2 - 7.3 = -.1 -.1/.8 = -1/8 = -.125
anonymous
  • anonymous
and then: -0.125/0.80 =-0.15625
amistre64
  • amistre64
no, there is no need to divide it again by .8
anonymous
  • anonymous
ok, i see it. ok next step.
amistre64
  • amistre64
\[z=\frac{x-\bar x}{\sigma}\] \[z=\frac{7.20-7.30}{0.80}\] \[z=\frac{-0.10}{0.80}=-0.125\]
amistre64
  • amistre64
id go with the z=.13 value, but a better result would be that since this is exactly in between .12 and .13 to take the average of the values as well
anonymous
  • anonymous
lets go with -0.13
amistre64
  • amistre64
lets :)
anonymous
  • anonymous
now I go find it in the table.
amistre64
  • amistre64
yep, we need the value for this z to calculate with
anonymous
  • anonymous
0.0517
amistre64
  • amistre64
thats what i got in my table as well
anonymous
  • anonymous
so do we take 0.5000+0.0517?
amistre64
  • amistre64
we do, and you understand why right?
anonymous
  • anonymous
because it is greater, and because it is a positive number
amistre64
  • amistre64
close enough, with more practice it should become better to see it :)
anonymous
  • anonymous
lol, I'm a begginer.
amistre64
  • amistre64
one way to think of it is to get the value to the left and subtract it from the total value under the curve; the total is 1
amistre64
  • amistre64
1 - (value to the left of z) = (value to the right of z)
anonymous
  • anonymous
because the problem is a greater than, so you have to add the left side of the bell with the amount that is greater than the half.
amistre64
  • amistre64
yep, that is a very good way to view it. good job ;)
anonymous
  • anonymous
well thanks for the medal! (medals).
amistre64
  • amistre64
and remember its asking for %
anonymous
  • anonymous
so we get 0.5517
anonymous
  • anonymous
which makes it a 55.17%
amistre64
  • amistre64
good
anonymous
  • anonymous
Ok, I have 2 more questions I need help with, and as I am learning maybe i can do most of the work. So here we go to another question, if your p for it.
amistre64
  • amistre64
im good for it .... :)

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