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Stels [109]
3 years ago
10

Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they ar

e normal random variables with means of 50 minutes, 60 minutes, and 40 minutes, respectively. The standard deviations are 15 minutes, 20 minutes, and 10 minutes, respectively. a Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object.
Mathematics
1 answer:
belka [17]3 years ago
8 0

Answer:

The mean of the total repair time is 150 minutes.

The variance of the total repair time is 725 minutes^2.

Step-by-step explanation:

To solve this problem, we have to use the properties of the mean and the variance. Our random variable is the sum of 3 normal variables.

In the case, for the mean, we have that the mean of the sum of 3 normal variables is equal to the sum of the mean of the 3 variables:

y=x_1+x_2+x_3 \\\\E(y)=E(x_1+x_2+x_3)=E(x_1)+E(x_2)+E(x_3)\\\\E(y)=50+60+40=150

For the variance, we apply the property for the sum of independent variables (the correlation between the variables is 0):

V(y)=V(x_1)+V(x_2)+V(x_3)\\\\V(y)=s_1^2+s_2^2+s_3^2\\\\V(y)=15^2+20^2+10^2\\\\V(y)=225+400+100\\\\V(y)=725

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If point Q(3,-4) is rotated +270° about the origin, what are the coordinates of Q?
erica [24]

Answer:

Q' =(-4,-3)

Step-by-step explanation:

Given

Q = (3,-4)

Rotation = +270 degrees

Required

Determine the new coordinates of Q (i.e. Q')

When a point (x,y) is rotated +270° about the origin, the new coordinates is: (y,−x)

So:

Q = (3,-4)

Where:

x = 3 and y = -4

Q' will be:

Q' =(-4,-3)

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2 years ago
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5 0
3 years ago
Ray UW is the angle bisector of Angle VUT. If the measure of Angle VUW = (4x + 6)° and the measure of Angle WUT = (6x – 10)°, wh
Lunna [17]

Hello! :)

Answer:

\huge\boxed{38^{\circ}}

--------------------------------------------------------------------------

An angle bisector divides an angle in half, therefore:

m∠VUW ≅ m∠WUT

Set the expressions equal to each other:

4x + 6 = 6x - 10

Subtract 4x from both sides:

6 = 2x - 10

Add 10 to both sides:

16 = 2x

Divide 2 from both sides:

x = 8.

Substitute in the value of "x" into the equation for ∠WUT:

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3 0
2 years ago
Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, w
WINSTONCH [101]

Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem, the values of the parameters are given as follows:

n = 6, p = 0.5.

The probability that fewer than 3 of them are boys is given by:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156

P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938

P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438

0.3438 = 34.38% probability that fewer than 3 of them are boys.

More can be learned about the binomial distribution at brainly.com/question/24863377

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7 0
2 years ago
The height and radius of a right cylinder are each 8 cm. what is its volume
NNADVOKAT [17]
The volume is going to be 12
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3 years ago
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