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2 years ago

-2x + 7 = x-32 i need all the steps

Mathematics

1 answer:

ycow [4]2 years ago

5 0

Answer:

-2x + 7 = x-32

7+32=x+2x

39=3x

x=39/3

x=13

Step-by-step explanation:

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and are independent Gaussian (Normal) random Variables. has mean 13.9 and variance 5.2; has mean 6.9 and variance 3.8. . (a) Cal

omeli [17]

This question is incomplete, the complete question is;

X and Y are independent Gaussian (Normal) random Variables. X has mean 13.9 and variance 5.2; Y has mean 6.9 and variance 3.8. . (a) Calculate P( W> 10)

Answer:

P( W> 10) is 0.1587

Step-by-step explanation:

Given that;

X ⇒ N( 13.9, 5.2 )

Y ⇒ N( 6.9, 3.8 )

W = X - Y

Therefore

E(W) = E(X) - E(Y)

= 13.9 - 6.9 = 7

Var(W) = Var(X) + Var(Y) -2COV(X.Y)

[ COV(X,Y) = 0 because they are independent]

Var(W) = 5.2 + 3.8 + 0

= 9

Therefore

W ⇒ N( 7, 9 )

P( W > 10 )

= 1 - P( W ≤ 10 )

= 1 - P( W-7 /3 ≤ 10-7 /3 )

= 1 - P( Z ≤ 1 ) [ Z = W-7 / 3 ⇒ N(0, 1) ]

from Standard normal distribution table, P( Z ≤ 1 ) = 0.8413

1 - P( Z ≤ 1 ) = 1 - 0.8413 = 0.1587

Therefore P( W> 10) is 0.1587

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3 years ago

Consider the following hypothesis test. : : The following results are for two independent samples taken from two populations. Ex

I am Lyosha [343]

Answer:

$z = -1.53$ --- test statistic

$p = 0.1260$ --- p value

Conclusion: Fail to reject the null hypothesis.

Step-by-step explanation:

Given

$n_1 = 80$ $\bar x_1= 104$ $\sigma_1 = 8.4$

$n_2 = 70$ $\bar x_2 = 106$ $\sigma_2 = 7.6$

$H_o: \mu_1 - \mu_2 = 0$ --- Null hypothesis

$H_a: \mu_1 - \mu_2 \ne 0$ ---- Alternate hypothesis

$\alpha = 0.05$

Solving (a): The test statistic

This is calculated as:

$z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}$

So, we have:

$z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}$

$z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}$

$z = \frac{-2}{\sqrt{0.8820 + 0.8251}}$

$z = \frac{-2}{\sqrt{1.7071}}$

$z = \frac{-2}{1.3066}$

$z = -1.53$

Solving (b): The p value

This is calculated as:

$p = 2 * P(Z < z)$

So, we have:

$p = 2 * P(Z < -1.53)$

Look up the z probability in the z score table. So, the expression becomes

$p = 2 * 0.0630$

$p = 0.1260$

Solving (c): With $\alpha = 0.05$ , what is the conclusion based on the p value

We have:

$\alpha = 0.05$

In (b), we have:

$p = 0.1260$

By comparison:

$p > \alpha$

i.e.

$0.1260 > 0.05$

So, we fail to reject the null hypothesis.

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