Suppose that the rate of return on stocks is normally dis-tributed with mean of 9% and a standard deviation of 3%. If I pick five stocks at random, what isthe probability that at least two of them will have a return of more than 12%.?

The probability that at least two stocks will have a return of more than 12% is 0.1810.

Step-by-step explanation:

Let X = rate of return on stocks.

The random variable X follows a Normal distribution, N (9, 3²).

Compute the probability that a stock has rate of return more than 12% as follows:

**Use the z table for the probability.

The probability of a stock having rate of return more than 12% is 0.1587.

Now define a random variable Y as the number of stocks that has rate of return more than 12%.

The sample size of stocks selected is, n = 5.

The random variable Y follows a Binomial distribution.

The probability of a Binomial distribution is:

Compute the value of P (X ≥ 2) as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

Thus, the probability that at least two stocks will have a return of more than 12% is 0.1810.

step-by-step explanation:

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