An investment broker reports that the yearly returns on common stocks are approx

Question

An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent. On the other hand, the firm reports that the yearly returns on tax free municipal bonds are approximately normally distributed with a mean return of 5.2 percent and a standard deviation of 8.6 percent. Find the probability that a randomly selected

1.common stock will give a positive yearly return

2.common stock will give more than a 10 percent return

3.common stock will give a loss of at least 10 percet

Explanation / Answer

mean = 12.4 , s = 20.6

a)

P(x >0)
z = ( 0 - 12.4) / 20.6
= -0.602

we need to find p(z> -0.602)

P(x >0) = P(z > -0.602) = 0.7264

b)
P(x >10)
z = ( 10 - 12.4) / 20.6
= -0.116

we need to find p(z> -0.116)

P(x >10) = P(z > -0.116) = 0.5464

c)

P(x <10)
z = ( 10 - 12.4) / 20.6
= -0.116

we need to find p(z< -0.116)

P(x <10) = P(z < -0.116) = 0.4536

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