SOLUTION: 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 probabi

Question 285960: 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?
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%?
I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says "at least" or "no higher than" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
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.
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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..
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b) What is the probability a company will have a stock price no higher than $20?
z(20) = (20-30)/8.2 = -1.2295
Note: Here you are finding the area to the left of -1.2295.
Because of symmetry the answer is the same as for "a".
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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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Cheers,
Stan H.
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I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says "at least" or "no higher than" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!!

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