Question

Suppose that X is a Normal random variable with mean 1.2 and standard deviation 0.5.

a. Find a value a such that P(X?a)=0.10.

b. Find a value b such that P(X?b)=0.10.

c. Find a value c such that P(1.2?c<X<1.2+c)=0.30.

Answer 1

Here we have

a:

Using excel function "=NORMSINV(0.1)", the z-score that has 0.10 area to its left is -1.28.

That is

We need to find a such that

The required a is

(b)

Using excel function "=NORMSINV(0.9)", the z-score that has 0.90 area to its left is 1.28.

That is

We need to find b such that

The required a is

(c)

Here we need z-score that has 0.35 area to its left. Using excel function "=NORMSINV(0.35)", the z-score that has 0.35 area to its left is -0.385.

So,

So,