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Zina [86]
3 years ago
5

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Su

rveying 2828 people to determine which statistics courses they have taken.
Mathematics
2 answers:
dlinn [17]3 years ago
7 0

Answer:

No, the given procedure doesn't result in a binomial distribution.

Step-by-step explanation:

We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.

Condition 1: Each observation should be independent, it must not depend on the result of previous observation.

Condition 2: The probability of success should stay same from trial to trial.

Condition 3: n is fixed (the number of observations)

Condition 4: There are only two outcomes success or failure.

Surveying 2828 people to determine which statistics courses they have taken.

Condition 3 is satisfied since n is fixed

Condition 1 is satisfied since each observation is independent

Condition 4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).

IRINA_888 [86]3 years ago
3 0

Answer:

No, the given procedure doesn't result in binomial distribution.

Step-by-step explanation:

For any procedure to be a binomial distribution, these below four conditions should be met;

<u>Condition 1</u>: Each and every observation should be independent from the other observations.

<u>Condition 2</u>: The probability of success(p) should always be same for each trial.

<u>Condition 3</u>: Number of trials(n) must be fixed.

<u>Condition 4</u>: There must be only two outcomes success or failure.

Now, the procedure given to us is : Surveying 2828 people to determine which statistics courses they have taken.

In this procedure;

  • Condition 1 is satisfied since each observation is independent from other.
  • Condition 3 is satisfied as n is fixed for surveying 2828 people.
  • Condition 4 is not satisfied because there can be more than 2 answers from the people regarding which statistics courses they have taken as there as many statistics courses.

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Remainder of question:

Find the probability distribution of x

Answer:

The random variable x is defined as: X = {0, 1, 2, 3, 4}

The probability distribution of X:

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P(X = 1) = 0.2916

P(X= 2) = 0.0486

P(X=3) = 0.0036

P(X = 4) = 0.0001

Step-by-step explanation:

Sample size, n = 4

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q = 0.9

Probability distribution of x,

P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) =  (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001

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8 0
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What is the product?
ZanzabumX [31]

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The product is:

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Step-by-step explanation:

For this problem you need to multiply the first row only for the two first column of the others matrix and get the desired result:

\left[\begin{array}{ccc}1&3&1\\-2&1&0\end{array}\right] \times \left[\begin{array}{cc}2&-2\\3&5\\4&1\end{array}\right]

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\left[\begin{array}{cc}15 & 14\\-1 & 9\end{array}\right]

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