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boyakko [2]
2 years ago
13

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X . What are the mean and s

tandard deviation of W ?
Mathematics
2 answers:
patriot [66]2 years ago
6 0

Answer:

The mean and standard devaition of W are 6 and 31 respectively.

Step-by-step explanation:

Given that:

W = 7 + 2X

Variance (W) = Variance(7 + 2X)

For a term constant term, the variance is zero.

So;

W = Var (2X)

W = 4 × Var(X)

W = 4 × (SD (X))²

W = 4 × (3)²

W = 4 × 9

W = 36

Thus, Variance (W) = 36

The standard deviation of W = \sqrt{variance}

W = \sqrt{36}

W = 6

Also;

E(W) = E(7 +2 X)

E(W) = 7 + 2 × E(X)

where;

mean X = 12

E(W) = 7 + 2(12)

E(W) = 31

Thus, the mean and standard devaition of W are 6 and 31 respectively.

Ivan2 years ago
4 0

Answer:

The mean is 31, and the standard deviation is 6.

Step-by-step explanation:

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choli [55]
360:100 or 360 to 100
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3 years ago
The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle
djyliett [7]
Here is your answer > >

Width of rectangle =15 inches

Length of rectangle =?

Diagonal of rectangle = 25 inches

We know that

(Diagonal of rectagle)^2=length^2+breadth^2

(25)^2=l^2+(15)^2

625=l^2+225

l^2=625-225

l^2=400

l=Root 400

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Hope it helps!

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Bebrainly
6 0
3 years ago
NEED ASAP CORRECT ANSWER GETS BRAINLIESt
andriy [413]

Answer:

QS = 8x - 2

Step-by-step explanation:

QS = QR + RS

QS = 6x - 11 + 2x + 9

QS = 8x - 2

8 0
3 years ago
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa
4vir4ik [10]

Using the z-distribution, it is found that since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is <u>tested if the mean length of jail time is still of 2.5 years</u>, that is:

H_0: \mu = 2.5

At the alternative hypothesis, it is <u>tested if it has increased</u>, that is:

H_1: \mu > 2.5

We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • \sigma is the standard deviation of the sample.
  • n is the sample size.

For this problem, the values of the <u>parameters</u> are: \overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26

Hence, the value of the <u>test statistic</u> is:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}

z = 1.7

The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u>, is of z^{\ast} = 1.645

Since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

A similar problem is given at brainly.com/question/24166849

5 0
2 years ago
Type the correct answer in the box.
riadik2000 [5.3K]

Hola USER___________

here is YOUR answer..!!

__________________

Quadratic Equation

The equation ...

Y = 5x^2 - 30x + 95

can be written as ..

5 0
3 years ago
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