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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.

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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Then add $50 + $3.50.

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2 years ago

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4 years ago

Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ

viktelen [127]

Answer:

(a) The critical number of $f(x)$ are $x=-4, 1$

(b)

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
Increasing for $(1, \infty)$

(c)

relative maximum $(-4, 112)$
relative minimum $(1, -13)$

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is $(-\infty, \infty)$ . Thus:

$\frac{df(x)}{dx} = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}$

(b)

A function $f(x)$ defined on an interval is monotone increasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)$

A function $f(x)$ defined on an interval is monotone decreasing on $(a, b)$ if for every $x_1, x_2 \in (a, b): x_1$ implies $f(x_1)>f(x_2)$

Combining the domain $(-\infty, \infty)$ with the critical numbers we have the intervals $(-\infty, -4)$ , $(-4, 1)$ and $(1, \infty)$ . Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

Increasing for $(-\infty, -4)$
Decreasing for $(-4, 1)$
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relative maximum $(-4, 112)$
relative minimum $(1, -13)$

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3 years ago

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