Question

) Suppose a random sample Y1, ..., Y100 are from the standard normal population N(0, 1).

(a) Write down the distribution of Y¯

(b) calc the probability Pr(Y¯ < 0.1)

(b) Calculate the probability Pr(Y¯ > a) = 0.9.

*the bar beside the Ys are supposed to be above them

Answer 1

Y1, ..., Y100 are from the standard normal population N(0, 1).

E( Y¯) = E(Y) = 0

V( Y¯ ) = V(Y)/sqrt(n) = 1/10 = 0.1

(a) Write down the distribution of Y¯

Y¯ ~ N(0,0.1)

(b) calc the probability Pr(Y¯ < 0.1)

(b) Calculate the probability Pr(Y¯ > a) = 0.9

We know that Pr(Y¯ > -0.8413) = 0.9