# Math Help - Normal distribution.

1. ## Normal distribution.

Hi there!
I am hoping you are able to help me as I am struggling to figure out on getting the answers for 2 questions.

Normal Prob. Distribution.

QUESTION ONE ( u = mean, and s= standard deviation)

Offspring plant produced 0.75 red.
100 seeds germinated and (x) is the number plants with red.

a) what is the exact. prob. distri. for (x) ?

Well i thought i wld use, P( z = (x - u) / s)
So, P = 0.75 , n = 100 and (x) is unknown.
u=np so, 100 times .75 = 75 as the mean
s=sqrt(npq) = sqrt(100x.75x.25)=sqrt(18.75)= therefore s=4.33
P(z=75-75/4.33) = ????????? equals 0. thats where im lost??? or should (x) = 74.5 ??????
and i shld be using the table however need the right answer...

b)Is it appropriate to approx the distri. in part a) using the normal distri. explain.

I said yes? but i cant even do the first question. but using the formula will give the probability under the curve????

d) what is the prob. that 53 or fewer offsprin plants have red. is it unusual occurence?

53 - 75 / 4.33 = -5.08 and using the table = 0.00 etc. which cant be right. Please help.

e) if you actually observe 53 of 100 offsprin plant with red. and are certain the ratio 3:1 was right. what other explanation cld you giv for this unusual occurence.

QUESTION 2. sampling distributions

p = .85 n = 500

a) what is the mean and standarad deviation of P.

im assuming i wld use u=np and the standard dev. formulas? yes??

b) is the distribution of P approx normal?

im assuiming yes? what forumal do i use? is it,
P( z = (x - u) / s) OR z = ( x - u ) / ( s / sqrt(n) )
help pls!!!

c) what is the prob. the sample proportion P exceeds .82

d) what is the prob that is lies between .83 and .88

e) .99 of the tme, the sample proportion wld lie between what two limit?
. Really need help on this, hopefully you can answer these questions.

Maths curious!

2. Originally Posted by Jon123
a) what is the exact. prob. distri. for (x) ?

You can assume X is N(75,18.75)

Originally Posted by Jon123
b)Is it appropriate to approx the distri. in part a) using the normal distri. explain.

Apply the C.L.T here, is your n big enough?

Originally Posted by Jon123

d) what is the prob. that 53 or fewer offsprin plants have red. is it unusual occurence?
Now you can use the table! Use P(z < (x-75)/s)

Use this guy P(z < (x-75)/(s/sqrt(n)) when finding the probability of the mean only