Question

Find a number Z so that P{ N(4, 4) < Z } = .75 ( the probability that a normal 4, 4 is less than Z
equals .75)
can you show steps to see how you did it thanks

Answer 1

is your notation N(\(\mu,\sigma^2\)) or N(\(\mu,\sigma\))

Answer 2

2nd one

Answer 3

so the mean is 4 and the standard deviation is 4

Answer 4

yes

Answer 5

your notation for the problem is not very nice...I'm going to modify it a little and you tell me if it is kn to you

Let \(X\) have a normal distribution with mean 4 and standard deviation 4


you wint to find the value of \(x\) such that

\[P(X\le x)=.75\]

Answer 6

*want to find...

Answer 7

um i dont even know how to start it

Answer 8

are you ok with how I worded the problem?

Answer 9

so the z score is .7734

Answer 10

yes

Answer 11

where do you get that?

Answer 12

I see what you did...no that is not correct

Answer 13

you need to go backwards from what you just did

Answer 14

what do you mean backwards

Answer 15

\[P(X\le x)=.75\]

\[\Rightarrow P\left(\frac{X-4}{4}\le \frac{x-4}{4}\right)=.75\]

\[\Rightarrow P\left(Z\le \frac{x-4}{4}\right)=.75\]

\[\Rightarrow P\left(Z\le z\right)=.75\]

looking up on a table (or a good calculator) one should get z=.6745

Answer 16

my calculator says it is z=.67448974945

Answer 17

but \[z=\frac{x-4}{4}\]

solve for x gives

\[x=4z+4\]

plugging in the value of z from above and we get

\[x=6.6979589978\]

Answer 18

how do you figure the z cause when i look for 0.75 i get o.7734

Answer 19

you are looking it up wrong...the .75 is a probability ...look in the middle of the table for a number that is closest to .75

Answer 20

oh that makes sense now k thanks

Answer 21

good