SOLUTION: The annual rate of return on investment in “Apple Company Fund” is normally distributed with mean of 20% and a standard deviation of 40%. (i) What is the probability that the

Algebra ->  Probability-and-statistics -> SOLUTION: The annual rate of return on investment in “Apple Company Fund” is normally distributed with mean of 20% and a standard deviation of 40%. (i) What is the probability that the       Log On


   

Question 1150680: The annual rate of return on investment in “Apple Company Fund” is normally distributed with mean of 20% and a standard deviation of 40%.
(i) What is the probability that the annual rate of return on investment in “Apple Company Fund” is between 5% and 50%?
(ii) Determine the annual rate of return such that the probability of exceeding it is 0.05.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i get the following.

mean is 20% and standard deviation is 40%.

probability the rate of return is between 5% and 50% is equal to .4195.

annual rate of return such that the probability of exceeding it is .05 would be 85.794%.

here are the visuals.

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if you don't have such a calculator as the one i used (found at http://davidmlane.com/hyperstat/z_table.html), then you might have to work with z-scores as shown below.

i)
z-score for annual rate of return of .05 is z = (5 - 20 / 40 = -.375.

z-score for annual rate of return of .5 is z = (50 - 20) / 40 = .75

area under the normal distribution curve to the left of z = -.375 = .35383.

area under the normal distribution curve to the left of z = .75 = .77337

area in between = .77337 - .35383 = .4195 rounded to 4 decimal places.

z-score that has area to the right of it of .05 is the same as z-score that has area of .95 to the left of it.

z-score with area of .95 to the left of it is equal to 1.64485.

raw score associated with that z-score is 1.64485 = (x - 20) / 40.

solve for x to get x = 1.64485 * 40 + 20 = 85.794.

i worked with percents, but you could also work with rates.

rate = percent / 100
percent = rate * 100

the z-score formula is z = (x - m) / s

z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation or the standard error.
in this case, standard deviation is used.