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
Alika [10]
3 years ago
14

A fair die is rolled 12 times. the number of times an even number occurs on the 12 rolls has

Mathematics
1 answer:
bonufazy [111]3 years ago
7 0

Answer:

Step-by-step explanation:

For a fair die, there are six likely options; 1, 2, 3, 4, 5, and 6

the probability of a even number is 3/6 = 0.5

Since the results of the die roll is independent and each trial is mutually exclusive, the distribution to explain the probability of occurrence will follow a binomial distribution such that n is the number of trials

x = number of successful throws

therefore for a Binomial distribution where

P(X =x) = nCx . P^x . (1-P)^ (n-x)

since p = 0.5, and n = 12, the distribution follows

P(X = x) = 12Cx . 0.5^x . (1 - 0.5)^(12- x)

= 12Cx . 0.5^x . 0.5)^(12- x)

where x = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)

since we are interested in the probability of the number of times an even number occurs

it can occur either as P(X = 0), P(X =1), P(X =2), P(X =3), P(X =4), P(X =5), P(X =6), P(X =7), P(X =8), P(X =9), P(X =10), P(X =11), and P(X =12)

For no even number in 12 rolls,

P(X = 0) = 12C0 . 0.5^0 . 0.5^(12- 0) = 0.000244

For one even number in 12 rolls,

P(X = 1) = 12C1 . 0.5^1 . 0.5^(12- 1) = 0.002930

For two even number in 12 rolls,

P(X = 2) = 12C2 . 0.5^2 . 0.5^(12- 2) = 0.016113  

For three even number in 12 rolls,

P(X = 3) = 12C3 . 0.5^3 . 0.5^(12- 3) = 0.053711  

For four even number in 12 rolls,

P(X = 4) = 12C4 . 0.5^4 . 0.5^(12- 4) = 0.120850

For five even number in 12 rolls,

P(X = 5) = 12C5 . 0.5^5 . 0.5^(12- 5) = 0.193359

For six even number in 12 rolls,

P(X = 6) = 12C6 . 0.5^6 . 0.5^(12- 6) = 0.225586

For seven even number in 12 rolls,

P(X = 7) = 12C7 . 0.5^7 . 0.5^(12- 7) = 0.193359

For eight even number in 12 rolls,

P(X = 8) = 12C8 . 0.5^8 . 0.5^(12- 8) = 0.120850

For nine even number in 12 rolls,

P(X = 9) = 12C9 . 0.5^9 . 0.5^(12- 9) = 0.053711

For ten even number in 12 rolls,

P(X = 10) = 12C10 . 0.5^10 . 0.5^(12- 10) = 0.016113

For eleven even number in 12 rolls,

P(X = 11) = 12C11 . 0.5^11 . 0.5^(12- 11) = 0.002930

For twelve even number in 12 rolls,

P(X = 12) = 12C12 . 0.5^12 . 0.5^(12- 12) = 0.000244

Final test summation[P(X)] =  1

i.e.

P(X = 0) + P(X =1) + P(X =2) + P(X =3) + P(X =4) + P(X =5) + P(X =6) + P(X =7) + P(X =8) + P(X =9) + P(X =10) + P(X =11) + P(X =12) = 1

Hence since 0.000244 + 0.002930 + 0.016113 + 0.053711 + 0.120850 + 0.193359 + 0.225586 + 0.193359 + 0.120850 + 0.053711 + 0.016113 + 0.002930 + 0.000244 = 1.000000,

the probability value stands

You might be interested in
Match each description to the appropriate provider or service.
lys-0071 [83]

Explanation:

<u>Urgent care centers</u>: care for basic needs after regular doctor hours

<u>Hospitals</u>: treat time-sensitive emergencies

<u>Medical specialists</u>: offer treatment in a specific field of medicine, such as cardiology

<u>General practice doctors and nurse practitioners</u>: care for routine medical needs

<u>Crisis pregnancy centers</u>: provide counseling for unplanned pregnancies

__

<em>Discussion</em>

Urgent care centers are often open all hours, but may not be as fully equipped (or staffed) to provide the sort of emergency medicine that a fully-equipped hospital can provide. While a general- or nurse-practitioner can provide routine care, they will consult with specialists when expertise is needed in a specific area.

Various kinds of pregnancy centers can provide counseling and perhaps some medical services for planned or unplanned pregnancies.

6 0
3 years ago
The histogram below shows the distribution of times, in minutes, required for 25 rats in an animal behavior experiment to naviga
tino4ka555 [31]

Answer:

c. The <em>median</em> and the IQR <em>(Interquartile range)</em>.

Step-by-step explanation:

Considering the histogram for the distribution of times for this experiment (see the graph below), we can notice that this distribution is skewed positively because of "<em>a few scores creating an elongated tail at the higher end of the distribution</em>" (Urdan, 2005). There is also a probable outlier (an animal that navigates around nine minutes). An outlier is an extreme value that is more than two standard deviations below or above the mean.

In these cases, when we have <em>skewed and extreme</em> <em>values</em> in a distribution, it is better to avoid using the <em>mean and standard deviations</em> as measures of central <em>tendency</em> and <em>dispersion</em>, respectively. Instead, we can use the <em>median</em> and the <em>interquartile range</em> for those measures.

With skewed distributions, the mean is more "sensible" to extreme data than the median, that is, it tends to not represent the most appropriate measure for central position <em>(central tendency)</em> in a distribution since in a positively skewed distribution like the one of the question, the mean is greater than the <em>median</em>, that is, <em>the extreme values tend to pull the mean to them</em>, so the mean tends to not represent a "reliable" measure for the central tendency of all the values of the experiments.

We have to remember that the dispersion measures such as the <em>standard deviation</em> and <em>interquartile range</em>, as well as the <em>variance</em> and <em>range</em>, provide us of measures that tell us <em>how spread the values are in a distribution</em>.

Because the <em>standard deviation depends upon the mean</em>, i.e., to calculate it we need to subtract each value or score from the mean, square the result, divide it by the total number of scores and finally take the square root for it, we have to conclude that with an inappropriate mean, <em>the standard deviation is not a good measure for the dispersion of the data, </em>in this case (a positively skewed distribution).

Since the median represents a central tendency measure in which 50% of the values for distribution falls below and above this value, no matter if the distribution is skewed, the median is the best measure to describe the center of the distribution in this case.

Likewise, the <em>quartiles</em> are not affected by <em>skewness</em>, since they represent values of the distribution for which there is a percentage of data below and above it. For example, the first quartile (which is also the 25th percentile) splits the lowest 25% of the data from the highest 75% of them, and the third quartile, the highest 25%, and the lowest 75%. In other words, those values do not change, no matter the extreme values or skewness.

For these reasons, we can say that the median and the interquartile range (IQR) describe the center and the spread for the distribution presented, and not the most usual measures such as the mean and standard deviation.

5 0
3 years ago
X = 7 + 3y
pogonyaev
<h3>Given Equation:</h3>

x = 7 + 3y

or, x - 3y - 7 = 0 ........ (i)

5x + 6y = 14

or, 5x + 6y - 14 = 0 .........(ii)

<h3>To Find:</h3>

The value of x and y.

<h3>Solution:</h3>

By dividing eq. ii by 2, we get

5/2x + 3y - 7 = 0 ........ (iii)

By adding eq. i and eq. iii, we get

15/2x = 0

or, <u>x = 0</u> ........(iv)

By putting eq.(iv) in eq. (i), we get

0 - 3y - 7 = 0

or, -3y = 7

or, <u>y = </u><u>-</u><u>7/</u><u>3</u>

<h2>Answer: ( 0, -7/3 )</h2>

The value of x and y is 0 and -7/3 respectively.

5 0
3 years ago
Read 2 more answers
I thought of an integer.if i multiply it by itself you will get 9.What is my number
ICE Princess25 [194]
The number is 3 because 3 multiplied by itself (3) is equal to 9.
3 0
2 years ago
Read 2 more answers
Write 5/6 as a decimal
Degger [83]

Answer:

0.83333333

Step-by-step explanation:

Is that what you wanted?

3 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP JUST NEED TO PASS THIS GEOMETRY TO BE DONE
    6·1 answer
  • Mr young has 30 times as many pencils as jack. The whole class has 200 times as many pencils as jack. If jack has 2pencils, how
    13·2 answers
  • Next value 4 D 7 G 10 J 13
    13·1 answer
  • Six times the sum of a number and 15 is -42
    14·1 answer
  • Gracie has 1/2 of a cantaloupe that she wants to divide. How many 1/10 's of a cantaloupe are there in 1/2 of a cantaloupe?
    14·1 answer
  • If P(A) = 0.2, P(B) = 0.2, and P(A ∪ B) = 0.4, then P(A ∩ B) = _______.
    15·1 answer
  • Find ln 0.985 using a calculator and round to four decimal places.
    5·2 answers
  • Find dy/dx given that y = sin x / 1 + cos x​
    14·1 answer
  • Let's make one thing clear. That thing you see in the mirror is you being garbage.
    15·1 answer
  • Hiii please help i’ll give brainliest if you give a correct answer please thanks!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!