Question

The price-earnings (PE) ratios of a sample of stocks have a mean value of 12.25 and a standard deviation of 3. If the PE ratios have a bell shaped distribution, use the 68-95-99.7 Rule to estimate the percentage of PE ratios that fall between:

A. 9.25 and 15.25.

Percentage =  %

B. 6.25 and 18.25.

Percentage =  %

C. 3.25 and 21.25.

Percentage =

NormalRandomVariables.

Answer 1

Solution :

Given that,

mean = = 12.25

standard deviation = = 3

Using Empirical rule,

a) P( - < x <   + ) = 68%

= P( 12.25 - 3 < x < 12.25 + 3 ) = 68%

= P( 9.25 < x < 15.25 ) =68%

  

b) P( - 2 < x <   + 2 ) = 95%

= P( 12.25 - 2 * 3 < x < 12.25 + 2 * 3 ) = 95%

=P( 6.25 < x < 18.25 ) = 95%

c) P( - 3 < x <   + 3 ) = 99.7%

= P( 12.25 - 3 * 3 < x < 12.25 + 3 * 3 ) = 99.7%

=P( 3.25 < x < 21.25 ) = 99.7%