Question

Suppose that a random variable Z has a standard normal distribution. Find a such that P(Z > a) = 0.204. Give your answer totwo decimal places. ?

Answer 1

Answer:

0.83

Explanation:

Since the probability P(Z > a) = 0.204< 0.5, 'a' must be lying on the right of zero. Draw the graph.

Find P(0 < Z < a).

$\begin{gathered} P(0a) \\ =0.5-0.204 \\ =0.296 \end{gathered}$

Find 'a' from the standard normal table.

From the table, P(0 < Z < 0.83) = 0.2967. Thus, 'a' approximately equals 0.83.