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