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Alona [7]
3 years ago
15

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 fiv

e stocks at random, what isthe probability that at least two of them will have a return of more than 12%.?
Mathematics
1 answer:
alisha [4.7K]3 years ago
6 0

Answer:

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

Step-by-step explanation:

Let <em>X</em> = rate of return on stocks.

The random variable <em>X</em> follows a Normal distribution, N (9, 3²).

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

P(X\geq 12)=1-P(X

**Use the <em>z</em> table for the probability.

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

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

The sample size of stocks selected is, <em>n</em> = 5.

The random variable <em>Y </em>follows a Binomial distribution.

The probability of a Binomial distribution is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, ...

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

P (X ≥ 2) = 1 - P (X < 2)

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

              =1-{5\choose 0}(0.1587)^{0}(1-0.1587)^{5-0}-{5\choose 1}(0.1587)^{1}(1-0.1587)^{5-1}\\=1-0.4215-0.3975\\=0.1810

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

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Answer:

Speed = 21.43m/s

Step-by-step explanation:

Given

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Time\ Recorded = 56s

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Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 meters ×80 meters
hjlf

Answer:

The route across the park is 40 meter shorter than the route around its edges.

Step-by-step explanation:

We have to calculate the distance for both routes

As the route around the edges is straight,  we have to find the sum of length of both edges

Let R_E be the distance of route around edges

R_E = 80+60 = 140\ meters

Now we know that a diagonal divides a rectangle in two right angled triangles in which the diagonal is the hypotenuse.

We can use Pythagoras theorem to find the length of the diagonal

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H^2 = P^2 + B^2

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Now

H^2 = (60)^2 + (80)^2\\H^2 = 3600+6400\\H^2 = 10000\\\sqrt{H^2} = \sqrt{10000}\\H = 100\ meters

In order to calculate that how much shorter is the path across the park, we have to subtract the distance across park from the distance across edges.

= 140-100 = 40\ meters

Hence,

The route across the park is 40 meter shorter than the route around its edges.

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Answer:

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He ran 11,420 miles on the weekend.

Step-by-step explanation:

It's simple: add 4610 and 6810 to get 11,420

hope this helped!

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