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

- anonymous

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- amistre64

A is asking: P(X<6.7)

- amistre64

B is asking P(X>7.2)

- amistre64

z = (6.7 - mean)/sd

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## More answers

- anonymous

6.7-7.30/0.80

- amistre64

good, thats our z score for A

- amistre64

we get a negative and we know that it wants the value of everything to the left of it

- amistre64

.5 - zvalue

- amistre64

zvalue will probably be called a Pvalue later in the book

- anonymous

-0.75

- amistre64

yep

- anonymous

Can we use the bell curve ?

- amistre64

we are .

- 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

somebody show how to proceed here

- anonymous

please

- anonymous

so 0.5000-0.2734(from the table)=

- 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

then work it into the question to find an answer

- amistre64

.2734 is good, so that should do it for A

- amistre64

B is trickier in that it wants values all to the right of z

- amistre64

same concept, but we have to adjust our thinking a little to accomodate for it

- anonymous

don't we do 0.5000-0.2734?

- amistre64

yes

- amistre64

A is the result of .5 - .2734

- anonymous

for the first one? right.

- amistre64

yep

- anonymous

oh ok, then i have 0.2266

- amistre64

good

- anonymous

so then I write it like this right?
P(x<6.7)=0.23

- amistre64

B needs some care taken to it.|dw:1320180861380:dw|

- amistre64

A asks for a % so we gotta rewrite .2266 as 22.66%

- anonymous

*100
.2266*100=22.66%

- amistre64

that looks good to me

- anonymous

ok, on to the second one!

- anonymous

are you still here?

- amistre64

im here

- amistre64

lets figure the z score to get started

- anonymous

ok, I have been having loading problems, so I thought it was me.

- anonymous

ok

- anonymous

P(x>7.2)

- anonymous

wait I am trying to figure it.

- amistre64

z = (7.2-7.3)/.8 .... same process, different numbers

- anonymous

x-mean/stan dev.
7.20-7.30/0.80

- anonymous

-01/0.80
-0.125/0.80
-0.15625

- amistre64

got some typos in there... but your on the right track
-.1/.8 = -.125

- amistre64

7.2 - 7.3 = -.1
-.1/.8 = -1/8 = -.125

- anonymous

and then:
-0.125/0.80
=-0.15625

- amistre64

no, there is no need to divide it again by .8

- anonymous

ok, i see it. ok next step.

- amistre64

\[z=\frac{x-\bar x}{\sigma}\]
\[z=\frac{7.20-7.30}{0.80}\]
\[z=\frac{-0.10}{0.80}=-0.125\]

- 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

lets go with -0.13

- amistre64

lets :)

- anonymous

now I go find it in the table.

- amistre64

yep, we need the value for this z to calculate with

- anonymous

0.0517

- amistre64

thats what i got in my table as well

- anonymous

so do we take 0.5000+0.0517?

- amistre64

we do, and you understand why right?

- anonymous

because it is greater, and because it is a positive number

- amistre64

close enough, with more practice it should become better to see it :)

- anonymous

lol, I'm a begginer.

- 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

1 - (value to the left of z) = (value to the right of z)

- 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

yep, that is a very good way to view it. good job ;)

- anonymous

well thanks for the medal! (medals).

- amistre64

and remember its asking for %

- anonymous

so we get 0.5517

- anonymous

which makes it a 55.17%

- amistre64

good

- 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

im good for it .... :)

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