Question

X~ N(60, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let EX be the random variable of sums. Sketch the graph, shade the region, label and scale the horizontal axis for Ķ, and find the probability. (Round your answer to four decimal places.) P(X < 60) = .

Answer 1

Since we need to find probability that sample mean is less than 60 and the population mean given is 60. So,

Corresponding z score = 0

Hence,

P( $\small \overline{X}$ < 60) = 0.50