A financial analyst computed the ROI for all companies liste

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with a standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1500 companies listed on the exchange, how many are of interest to her?

Solution

P(0.14 < X < 0.16)

= P(X<0.16) - P(X < 0.14)

= P(Z < 0.16 - 0.1 / 0.05) - P(Z < 0.14 -0.1/0.05)

= P(Z<1.2) - P(Z<0.8)

= 0.8849 - 0.7881

= 0.0968

number of companies interest to her

= 0.0968 * 1500

= 145