Homework for stats

Quote:

Originally Posted by schinb64

I have some problems that I dont no what to do.

1) The gestation for a human baby is approximately normally distributed with the mean of 275 days. What is the standard deviation of this distrbution bility is .25 that the gestation period is more then 280 days?

Something has been lost in the typing here.

Quote:

2) The inside diameter of a cylindar tube is a random variable X w. mean of 3 in and a S.D. of 0.2 in and the thickness of the tube is a random variable Y w. the mean of 0.3 in and the S.D. of .005 the two random variables are independent Find the mean and the standard deviation of the outside diameter Z=X+2Y

to get the SD I take equation and put the S.D. in so i will get (0.2)^2+2(0.005)^2 then I take the answer that I get and take the Square root to get the new standard. How do I find the mean?

Any help is apprieciated. Thank you for your time.

Z is the sum of two independent normaly distributed random variables, so
its mean is the sum of the means, and its variance is the sum of the varianves, so:

Mean(Z) = Mean(X) + Mean(2Y) = Mean(X) + 2 Mean(Y) = 3+2 0.3 = 3.6 inches.

Var(Z) = Var(X) + Var(2Y) = Var(X) + 4Var(Y) = 0.2^2 + 4 0.005^2 = 0.0401

So SD(Z) = sqrt(Var(Z)) = 0.20025

RonL