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3 years ago

10

Mary drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Mary drove h

ome, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Mary live from the mountains?
Do not do any rounding.

1 answer:

ivann1987 [24]3 years ago

6 0

Speed = Distance ÷ time
Distance ÷ 6 - Distance ÷ 8 = 16
(8D - 6D) ÷ 48 = 16
2D = 16 x 48
2D = 768
D = 384 miles

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Step-by-step explanation:

Given

$p_1 = 5\%$

$p_2 = 85\%$

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$n = 20$

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Solving (a): Names and values of joint pdf of X, Y and Z

Given that:

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$Y \to$ Number of voids considered as medium slabs

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The parameters are:

$p_1 = 5\%$ $p_2 = 85\%$ $p_3 = 10\%$ $n = 20$

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Solving (b): The range of the joint pdf of X, Y and Z

Given that:

$n = 20$

The number of voids (x, y and z) cannot be negative and they must be integers; So:

$x + y + z = n$

$x + y + z = 20$

Hence, the range is:

$\{(x,y,z)| x + y + z=20\}$

Solving (c): Names and values of marginal pdf of X

We have the following parameters attributed to X:

$p_1 = 5\%$ and $n = 20$

Hence, the name is: Binomial distribution

Solving (d): E(x) and Var(x)

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$p_1 = 5\%$ and $n = 20$

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However, the given values of x in this question implies that:

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$x + y + z = 21$

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$P(X = 1, Y = 17, Z = 3) = 0$

So:

$P(X \le 1, Y = 17, Z = 3) =P(X = 0, Y = 17, Z = 3) +0$

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Expand

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$P(X=0; Y=17; Z = 3) = 20*19*3 * (85\%)^{17} * (10\%)^{3}$

Using a calculator, we have:

$P(X=0; Y=17; Z = 3) = 0.07195$

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