# Thread: Two questions I'm stuck on

1. ## Two questions I'm stuck on

Hey, if you could help me out with these two questions that would be great!!!

1. X has a binomial distribution. P = 0.4 and there are 35 trials.
a) Find P(X=20)
b) Find P(X>=20)

c) Find the variance of X

d) Find the expected value of X

e) Approximate P(X>=20) using the normal distribution..

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2. You have applied for an export grant from the Federal Government. There are two types of grants: A and B. You estimate that you have a 70% chance of receiving a type A grant and a 40% chance of receive a type B grant. If you receive a type A grant, there is a 90% chance of receiving a type B grant.

a) What is the likelihood of receiving a type A AND type B grant?

b) What is the likelihood of receiving at least one grant?

c) If you receive a type B grant, what is the probability of receiving a type A grant?

Thanks

2. Originally Posted by cce78
Hey, if you could help me out with these two questions that would be great!!!

1. X has a binomial distribution. P = 0.4 and there are 35 trials.
a) Find P(X=20)
b) Find P(X>=20)

c) Find the variance of X

d) Find the expected value of X

e) Approximate P(X>=20) using the normal distribution..
X has a binomial distribution B(0.4,35), so:

P(X=n) = 35!/(n! (35-n)!) 0.4^n 0.6^(35-n)

so:

a) P(X=20) = 35!/(20! (15)!) 0.4^20 0.6^15 = 0.016791

b) P(X>=20) = sum_{n=20 to 35} 35!/(n! (35-n)!) 0.4^n 0.6^(35-n) ~= 0.030

c) You should know that the variance of a binomial RV is N p (1-p), so in this case
the variance is 8.4

d) you should know that the mean of a binomial RV is Np, so in this case is 14.

e) Using the normal approx we want the probability that a standard normal RV
exceeds a z score of:

z = (19.5-14)/sqrt(8.4) = 1.90

which is 0.0287.

RonL