The average stock prices for companies making up the S&P 500 is k30 and the standard deviation is k8.2. Assume the stock prices are normally distributed. How high does a stock price of a company have to be to be put in the top 10%?
(z - Value for p = 0.4 is 1.29)
To find the stock price that puts a company in the top 10%, we need to calculate the z-score for the top 10% and then convert it back to the actual stock price.
To find the z-score, we use the formula:
z = (x - μ) / σ
where:
x is the stock price,
μ is the mean stock price, and
σ is the standard deviation.
Given:
Mean (μ) = k30
Standard Deviation (σ) = k8.2
p = probability = 0.4 (10% = 1 - 0.10 = 0.90)
We are looking for the z-score that corresponds to a probability of 0.40, which is 1.29.
1.29 = (x - 30) / 8.2
Solving for x:
1.29 * 8.2 = x - 30
10.578 = x - 30
x = 40.578
Therefore, the stock price of a company must be higher than $40.578 to be put in the top 10%.