Z Table Question...but not even sure where to start!

Question

The return on a stock is the change in its market price plus any dividend payments made.

Total return is usually expressed as a percent of the beginning price. Excluding the three low outliers,

the average return of the remaining 369 months is 0.84% with a standard deviation of 4.097%. If the

distribution of the 369 months (excluding the outliers) were exactly N(0.84, 4.097), what would be the

proportion of months with returns greater than:

a) 0%;

b) 4%?

Answer 1

Recall the formula for the z-score: z = (x- mean)/stndDev

Prob(x < 0) = Prob ( z < (0-0.84)/4.097))

= Prob(z < 0.2050280693190139126189895045155.....)

=0.418775097 <--- use normal table or =normdist from MS Excel

Prob(x < 4) = Prob ( z < (4-0.84)/4.097))

= Prob( z < 0.77129607029533805223334146936783....)

= 0.779734269