X1, . . . ,X9 are independent and identically distributed random variables?

X1, . . . ,X9 are independent and identically distributed random variables


each with a N(4, 25) distribution. Write down the distribution of


the sample mean ¯X and hence find the probability it is


(a) less than 5,


(b) greater than 5.8,


(c) between 3.5 and 4.4.

X1, . . . ,X9 are independent and identically distributed random variables?
since the underlying distribution is normal, you can use a normal distribution:





E(X) is estimated by the mean of the underlying distribution


V(X) is estimated by Var(X)/n = 25/9





Then you run it like standard normal...