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.

she will most likely have 33  

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this