Question

A client has an investment portfolio whose mean value is equal to $1,000,000 with a standard deviation of $30,000. He has asked you to determine the probability that the value of his portfolio is betweern $970,000 and $1,060,000. 0.1587 0.0228 0.1359 0.8185

Answer 1

$\mu$ = 1,000,000

$\sigma$ = 30,000

To find P(970,000 < X < 1,060,000):

Case 1: For X from 970,000 to mid value:

Z = (970,000 - 1,000,000)/30,000 = - 1

Table of Area Under Standard Normal Curve gives area = 0.3413

Case 2: For X from mid value to 1,060,000

Z = (1,060,000 - 1,000,000)/30,000 = 2

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(970,000 < X < 1,060,000) = 0.3413 + 0.4772 = 0.8185

So,

Correct option:

0.8185