solve the following its about RANDOM SAMPLES

(3) Suppose a batch of steel rods produced at a steel plant have a mean length of 150 millimeters, and a standard deviation of 12. If 100 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.5 millimeters? (4) Evans and Rosenthal, 2009] Let X1, X2, ... be a sample from a population that is geometrically distributed with p = 1. (a) Use a suitable version of the Central Limit Theorem to estimate the probability 800 P E X 2 2450 1=1 (b) The negative binomial random variable was defined as a sum of a sample of geometric random variables. Why might this approach be preferable to just using the negative binomial PMF