Advanced Stats Help
I've been struggling on these two questions. Any help would be greatly appreciated.
1) a)Let X be a population with mean 75 and variance 25. Find the probability that in a random sample of size 64 the sample mean will be between 74 and 77.
b)If X is a normal population find the porability that the sample standard deviation will be between 4.5 and 6.
2)Using the probability transform theorem, please simulate a random sample of size 5 from a normal population with mean of 81 and standard deviation of 6
Re: Advanced Stats Help
Hint: The distribution of (mu - mu_hat)/sigma ~ N(0,1) given that you have a population Normal(mu,sigma^2) = Normal(75,25). Re-arrange to get the distribution of mu_hat and then solve for that probability.
Hint: for (b) do the same thing except look at the chi-square distribution where (n-1)S^2/sigma^2 ~ Chi-Square(n-1).