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Mama L [17]
2 years ago
15

According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down

in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 25 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.
What is the probability this could occur by chance? (Round your answer to 6 decimal places.)
Mathematics
1 answer:
TiliK225 [7]2 years ago
8 0

Answer:

The probability this could occur by chance is approximately 0.003053.

Step-by-step explanation:

This problem can be solved with a binomial distribution, if we imagine that by the end of January the stock market will follow the same pattern for the rest of the year we can define the following random variable:

X = "The stock market will be up for the rest of the year",

and X = 1 if by the end of January the stock market is up and X = 0 otherwise, this way X \sim Bin(1,p) \text{ or } X \sim Bernoulli(p), where p is the probability of success. Next we can define the following random variable:

Y = "Sum of all years where the stock market was up"

Now, the sum of a Bernoulli random variables is a Binomial random variable, in other words Y \sim Bin(n,p), where n is the number of trials and p is the probability of success. The pdf of Y is given by:

P(X = k) = \big {n \choose k}p^k(1-p)^{n-k}, \text{ } k \leq n

The question give us the n = 34, k = 25 and p = 0.5. Now we just have to solve it:

P(X = 25) = \big {34 \choose 25}(0.5)^{25}(1-0.5)^{34-25} = {34 \choose 25}(0.5)^{34} = \\P(X = 25)= 52451256\cdot(0.5)^{34} \approx 0.003053

Which is highly unlikely to happen.

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Plzzzzzzzz! A suitcase lock has a code 4 symbols long. The symbols on the lock are a star, a square, a circle, a triangle, a lin
34kurt

Answer:

                \dfrac{1}{30}

Step-by-step explanation:

6 symbols and 4-symbol code so number of combinations wich doesn't contain the same symbol twice would be:

6•5•4•3 = 360

If code starts with a star followed by triangle that means only one posibility for first two symbols and code doesn't containing the same symbol twice means that left 4 symbols for next two.

So number of combinations of code starting with a star followed by triangle and doesn't containing the same symbol twice will be:

1•1•4•3 = 12

The probability that a randomly chosen code starts with a star followed by triangle and doesn't contain the same symbol twice:

\dfrac{1\cdot1\cdot4\cdot3}{6\cdot5\cdot4\cdot3}=\dfrac{1\cdot1}{6\cdot5}=\dfrac{1}{30}

7 0
3 years ago
I need help figuring out the answers for this
Gennadij [26K]
<h2>Step-by-step explanation:</h2>

Interest, is an additional money paid for borrowing money. it could be simple or compound interest.

simple interest= p×T×R/100

when interest is compounded annually

F= p(1+r)^t

F= future value

p= principal

r= rate

t= time

compound interest is calculated based on the initial and accumulated interest.

<h2>interest Linda earns</h2><h3>fist year</h3>

F= p(n+r)^n

F= 10000(1+0.02)^1

F= 10000×1.02= $10200

interest= 10200-10000

interest = $200

second year

F = 10200(1+0.02)^1

F=10200×1.02= $10404

Interest= 10404-10200

interest= $204

third year

F= 10404(1+0.02)^1

F= 10404(1.02)

F = $10612.08

interest= 10612.08-10404

interest= $208.08

<h2>Bob's interest</h2><h2>I= p×t×R/100</h2>

first year

I=10000×1×0.02/100

interest= $2

second year

I= 10000×2×0.02/100

interest= $4

for the third year

I =10000×3 × 0.02/100

interest= $6

<h2>check answer above for final computation</h2>

6 0
2 years ago
Adam currently runs about 40 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run pe
BigorU [14]

Answer:

52 miles/week (12 more miles per week)

Step-by-step explanation:

In order to know the miles per week with this increasement, we'll use the rule of 3, assuming that 40 miles is the 100% innitially so:

If:

40 miles --------->100%

X miles ----------> 30%

Solving for X we have the following:

X = 30 * 40 / 100 = 12 miles

So, if Adam wants to increase his weekly mileage by 30%, he needs to run 12 more miles, and that makes a total of 52 miles/week

6 0
2 years ago
What is the solution to the system of equations of linear equations 2x + 4y = 38 and 10x + 3y = 105
nata0808 [166]
<span>A) 2x + 4y = 38
B) 10x + 3y = 105
Multiplying A) by -5
A) -10x -20y = -190 then adding it to B)
</span><span>B) 10x + 3y = 105

-17y = -85
y = 5
x = 9


</span>
6 0
3 years ago
How do I solve for y?
vivado [14]
Short Answer: y = 36°
Remark
What an interesting question!! The first thing you have to do is find out what the interior angle of a regular pentagon is. After you have done that, you can calculate y.

Method.
The exterior angles of a regular figure add up to 360°. 

Step One

Find out the size of the exterior angles of a  regular pentagon. 
There are 5 such angles. They add up to 360°

5x = 360  Divide by 5
x = 360 / 5
x = 72°

Step Two
Find out the value of the interior angles of a pentagon.

Method
The interior and exterior angles add up to 180°
Exterior Angle + Interior Angle = 180°
Exterior angle = 72 degrees
72° + Interior Angle = 180°                  Subtract 72 from both sides.
Interior Angle = 180° - 72° 
Interior Angle = 108°

Step Three
Solve for y.

There are 3 tiles each with an angle of 108° that are placed together. So y + 3 interior angles = 360°

y + 3*interior angles = 360°
y + 3*108 = 360 
y + 324 = 360 Subtract 324 from both sides.
y = 360 - 324
y = 36°

7 0
3 years ago
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