Statistics

1) (14pts) Consider a population with unknown mean ,u and 02 = 16. Suppose a sample of size 36 will be collected from this population. Let X be the mean of this sample and f(x) be the probability density function of 5'. Fill in the blank with the most appropriate relation of the following four (, =, \"depends on the situation\" (could be any one of these)). (a) E [1'7] _ 6 (b) The area under the curve (x u)2f(x) 16 (c) PO? 1) .5 (f) E [if 0 (g) P()?> 1ANDX