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%.
Z = (score-mean)/SD
Use same table.
89
0.334
0.2
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%.
To find the probability of a yearly return being greater than 6%, we need to calculate the z-score and then use a standard normal distribution table or a calculator to find the corresponding probability.
First, let's calculate the z-score using the formula:
z = (x - μ) / σ
where:
- x is the value we want to find the probability for (in this case, 6%)
- μ is the mean (5.1%)
- σ is the standard deviation (2.7%)
Plugging in the values:
z = (0.06 - 0.051) / 0.027 ≈ 0.3333
Now, we can consult a standard normal distribution table or use a calculator to find the probability associated with this z-score. The probability is the area under the normal curve to the right of the z-score.
Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution and calculate:
P(Z > 0.3333) ≈ 0.3694
Therefore, the probability of a yearly return being greater than 6% is approximately 0.3694 or 36.94%.