The average stock price for companies making up the S & P 500 is $30, and the st

Question

The average stock price for companies making up the S & P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed. A. What is the probability a company will have a stock price of at least $40.00 B. What is the probability a company will have a stock price no higher than $20? C. How high does a stock price have to be to put a company in the top 10%?

Explanation / Answer

a) What is the probability a company will have a stock price of at least $40? Find the z-score of 40. Formula: z(x) = (x-u)/s z(40) = (40-30)/8.2 = 1.2195 Note: That means 40 is 1.2195 standard deviations above the mean. ----------------------------- Having converted 40 to a z-score you find the area to the right of 1.2195 under the standard curve. P(x> 40) = P(z> 1.2195) You have to use technology or a z-chart to find the area to the right of 1.2195. I use a TI84 calculator and get normalcdf(1.2195,100) = 0.1113.. B)What is the probability a company will have a stock price no higher than $20? z(20) = (20-30)/8.2 = -1.2295 C)c) How high does a stock price have to be to put a company in the top 10%? Find the z-score that has a right tail of 10%. I use the TI to get invNorm(0.90) = 1.28155.. Use the formula x = zs + u x = 1.28155*8.2 + 30 x = $40.51 Stock prices above $40.51 are in the top 10% of the stock prices.

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