1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Which is least 1.3 1 1/3 or 1.34
Evgesh-ka [11]
1.3 is the least because ur supposed to add a zero so they can all be the same place value
5 0
3 years ago
Write as a product of two polynomials. <br><br> (x-y)^2-a(y-x)
Setler79 [48]

Answer:

\sf{(x-y)^2-a(y-x)} \\ = \sf{({x}^{2}  - 2xy +  {y}^{2} ) - (ay - ax)} \\

7 0
2 years ago
Read 2 more answers
Which of the following comparisons is FALSE?
dybincka [34]

Answer:

A

Step-by-step explanation:

Let's check each one-by-one.

a.

we know 3.79 liters is 1 gallon, so 4 liters IS NOT LESS THAN 1 gallon

THis is false.

b.

We know 1 feet is 0.30 meters, so definitely 1 foot is less than 1 meter.

This is true.

c.

we know around 28.35 grams is 1 ounce, so definitely 25 grams is less than 1 ounce.

THis is true.

d.

We know 1 km is approximately 0.62 miles so 10 km would be around 0.62*10 = 6.2 miles

So definitely 9 miles IS GREATER than 10 km.

THis is true.

So answer choice A is false, only.

4 0
3 years ago
Pls help me <br> plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Svet_ta [14]

Answer:

x ≤ 2

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
How do you find the range of a function?
NISA [10]
<span>For more difficult cases, it may be easier to draw the graph first using the domain if possible and then determine the range graphically.See if you can find the inverse function. The domain of a function's inverse function is equal to that function's range.<span>Check to see if the function repeats.</span></span>
8 0
3 years ago
Other questions:
  • The Height of the pyramid in the diagram is three times the radius of the cone.The base area of the pyramid is the same as the b
    5·1 answer
  • Whitch three capital letters have rotational symmetry but do not have line symmetry
    14·2 answers
  • What is the coefficient of the second term (B) of the trinomial? (6x+2)2 = 36x2+Bx+4
    11·1 answer
  • Match the following terms with their correct definition.
    7·1 answer
  • Solve by factoring 25x^2+1=10
    15·2 answers
  • Which table represents a linear function?<br>​
    11·2 answers
  • A)The function has two x-intercepts
    11·1 answer
  • B) Is the relation a function? Use the vertical line test to decide.
    8·1 answer
  • Work out the size of angle x.
    9·2 answers
  • Please help! <br> Use the table below to graph the function.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!