Statistics and Probability Answers

8023 offspring peas were obtained, and 24.94% of them had green flowers. the others had white flowers. consider a hypothesis test that uses a 0.05 significance level to test the claim that green flowered peas occur at a rate of 25%.
what is the test statistic?
what is the critical value?
what is the p value?
what is the conclusion?
can a hypothesis test be used to prove that the rate of green flowered peas is 25%, as claimed?

the effect on an antidepressant drug varies from person to person.suppose that the drug is effective on 80% of women and 65% of man.it is known that 66% of the women who take the drug are women.

i) what is the probability that the drug is effective?
ii) suppose that you are told that the drug is effective.what is the probability that the drug taker is a man..?

Let X be given by its "distribution" function F(x), such that:

F(x) = 0 if x ≤ 0
F(x) = (x^2)/4 if 0<x≤2
F(x) =1 if x>2

Find E(x), var (x) and std deviation (x).

The density function of a random variable X is given by

f(x)= 1/(7√2π) e^((x+3.6)^2)/98)

Find its (a) math expectation, (b) variance and (c) distribution function.

Find the density function of a normally distributed random variable X, if E(X) = 7.8 and σ(X) = 4.1

The distribution of the width of a standard piece of computer paper is normal with an expectation of 8.5 inches and the standard deviation of 0.2 inch.
a) Find the probability that the width of any given piece of computer paper is between 8.40 and 8.55.
b) Find the probability that the width of any given piece of computer paper is less than 8.35.
c) Find the probability that the width of any given piece of computer paper is greater than 8.6.

Find E(X) , var (X), and std deviation (x) if a random variable X is given by its density function f(x) , such that
f(x)=0, if x≤1
f(x)=(3/8) (x^2), if 0<x≤2
f(x)=0, if x>2

I have a biased coin that lands heads with probability p and start with an empty urn. I flip the coin n times. Each time the coin lands heads, I add a blue ball to the urn. Each time the coin lands tails, I add a green ball to the urn. After I finish flipping the coin and without knowing the composition of the urn, you draw k balls from the urn one at a time, replacing each ball you draw before drawing another one. If all k of the balls that you draw are blue, what is the probability that all n balls in the urn are blue?

Two bags marked M and N contain identical pen drives. Bag M contains 10 green pen drives and 8 red pens drives. Beg N contains 7 green pen drives and 6 red pen drives. A pen drive is randomly selected from bag M and put into bag N. Then, another pen drive is randomly selected from bag N.
(a) If a red pen drive is selected from bag N, find the probability a green pen drive is selected from bag M.

It’s known that a random variable X is distributed normally with E(X) = 3

and it’s also known that p(0≤X≤1)+p(5≤X≤6) = 0.6. Find p(p(5≤X≤6).