Question

Let X be a Gaussian(2,4) random variable. What is the probability that X falls between 0 and 1? Write your answer as a decimal with two decimal places.

Note 0.15 is incorrect

Answer 1

Correct answer:

0.09

EXPLANATION:

= 2

To find P(0 < X < 1):

Case 1:

For X from 0 to mid value:

Z = (0 - 2)/2 = - 1

Table of Area Under Standard Normal Curve gives area = 0.3413

Case 2:

For X from 1 to mid value:

Z = (1 - 2)/2 = - 0.5

Table of Area Under Standard Normal Curve gives area = 0.1915

So,

P(0 < X< !) = 0.3413 - 0.1915 = 0.1498

So,

P(0<X<1)= 0.15

Since the answer = 0.15 is given as incorrect, we note the following interpretation of Gaussian (2,4):

Though generally G(2,4) is interpreted as:

Mean = = 2

Variance = = 4,

Since the answer = 0.15 is given as wrong, we note the following interpretation of G(2,4) by some authors:

= 2

= 4

(EXPLANATION: Some authors take G(2,4) as mean = 2 and SD = 4)

To find P(0 < X < 1):

Case 1:

For X from 0 to mid value:

Z = (0 - 2)/4 = - 0.5

Table of Area Under Standard Normal Curve gives area = 0.1915

Case 2:

For X from 1 to mid value:

Z = (1 - 2)/4 = - 0.25

Table of Area Under Standard Normal Curve gives area = 0.0987

So,

P(0 < X< !) = 0.1915 - 0.0987 = 0.0928

So,

P(0<X<1)= 0.09

So,

Answer is:

0.09