What is the value of A such that PZ A 05 Answer to two dec

What is the value of A such that P(Z > A) = .05? Answer to two decimal places.

The answer is 1.65 but the solution doesn\'t make any sense to me. How did they come on 0.5?

Solution: p(z>a) = 0.05
P(a<z<0) = 0.5 - 0.05 = 0.45
So a = -1.645 or -1.65

Solution

P(Z > a) = 0.05 has the solution a = 1.65. So you are correct.

However, check for misprints or a error in reading.

They might have asked:

P(Z < a) = 0.05, what is a?

And they may have provided probability values between Z and 0. [Like P(a<Z<0) = ...] where P(Z<0) = 0.5

P(a<Z<0) = P(Z<0) -P(Z<a) = 0.5 - P(Z<a)

So using that, for P(Z < a) = 0.05

a = -1.65

So, please check the sign.