The yearly returns of a stock are normally distributed with a mean of 5.1% and standard deviation of 2.7%. Find the probability of a yearly return being greater than 6%.
plug your data into this ...
http://davidmlane.com/hyperstat/z_table.html
click on "above" and enter 6
to get .3694
(that's very high SD )
To find the probability of a yearly return being greater than 6%, we need to calculate the area under the normal distribution curve to the right of 6%.
Here's how you can do that using the Z-score formula and a standard normal distribution table:
1. Calculate the Z-score for the value of 6%. The Z-score formula is: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. In this case, X = 6%, μ = 5.1%, and σ = 2.7%. Plugging in these values, we get: Z = (0.06 - 0.051) / 0.027.
2. Using the Z-score you just calculated, find the corresponding area under the normal distribution curve by referring to a standard normal distribution table. The Z-score will represent the number of standard deviations from the mean. In this case, the Z-score is positive since we're looking for the probability to the right of the mean.
3. Look for the Z-score in the table and find the corresponding area. This area represents the probability of a yearly return being less than 6%. Since we want the probability of a return being greater than 6%, subtract this area from 1.
That's how you can find the probability of a yearly return being greater than 6% using the Z-score formula and a standard normal distribution table.