Question

The area under the standard normal curve that lies to the left of -1.8 is 0.0359. Without consulting a the table giving areas under the standard normal curve, determine the area under the standard normal curve that lies to the right of 1.8.
answer:

b) Which property of the standard normal curve allowed you to answer part a)?

A. The standard normal curve extends indefinitely in both directions
B. The standard normal curve is symmetric about 0
C. Almost all the area under the standard normal curve lies between -3 and 3
D. The total area under the curve is 1
E. None of the above

Answer 1

We are given the area to left of Z_{​​​​​​1} = -1.8 , i.e.

P ( Z < -1.8 ) = 0.0359

we asked area to right of Z_{​​​​​​2} = 1.8 i.e P ( Z > 1.8 )

The standard normal curve is symmetric , so area to left of -1.8 and area to right of 1.8 is same

P( Z < - a) = P ( Z > a )

P( Z <-1.8 ) = P ( Z > 1.8 ) = 0.0359

So area to right of 1.8 is 0.0359

b ) Her we used the standard normal curve is symmetric about 0.