Question

(1 point) a) Fact the region under the standard normal curve that lies to the left of -1.92 has area 0.0274289. Without consulting a table or a calculator giving areas under the standard normal curve, determine the area under the standard normal curve that lies to the right of 1.92 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 total area under the curve is 1 C. Almost all the area under the standard normal curve lies between -3 and 3 D. The standard normal curve is symmetric about 0 O E. None of the above

Answer 1

Question 1a)

It is given that

The region under the standard normal curve that lies to the left of -1.92 has area 0.0274289.

Now, we have to find the area under the standard normal curve, that lies to the right of 1.92.

We know, from the property of normal distribution, that a standard normal curve is symmetric about zero.

This means, the area to the right of zero, is same as the area to the left of zero; ie.

$P(z<0)=P(z>0)$

And this also means

$P(z<-h)=P(z>h)$

Where, h is any real value.

So, when h=1.92, we can conclude that

$P(z<-1.92)=P(z>1.92)$

Now, it is given P(z<1.92)=0.0274289.

So, we can say

$P(z>1.92)=0.0274289$

The answer is

The area under the standard normal curve that lies to the right of 1.92 is 0.0274289.

Question 1b)

The property of standard normal curve that allowed us to answer part (a) is

option (D) The standard normal curve is symmetric about 0.