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A certain industrial process yields a large number of steel cylinder whose lengths are distributed normally with mean 3.25 inche

Taya2010 [7]

Answer:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.25,0.05)$

Where $\mu=3.25$ and $\sigma=0.05$

We slect two observations $X_1, X_2$

And let denote the combined lenght as:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

3 0

3 years ago

What are the domain and range of the graph? Is the graph a function? Explain.

kumpel [21]

Answer:

Domain: -3 < x <2

Range: -4 < y < 5

Is the graph a function? No the graph isn't not, since the graph fails the vertical line test

8 0

3 years ago

Sarah drives 1 2/3 hours on Monday. She drives 2 1/6 hours on Tuesday. How far does Sarah drive in those two days?

WINSTONCH [101]

Answer:

3 5/6

Step-by-step explanation:

I used a calculator on calculator soup it basically has every calculator

6 0

3 years ago

Read 2 more answers

What is the expanded form for 602,050,123

Fudgin [204]

600000000+2000000+50000+100+20+3

3 0

3 years ago

3x + 8 = -x + 20 What is x?

g100num [7]

First, lets take all the x values on one side.

3x + x + 8 = -x + x + 20
4x + 8 = 20

Now, lets put the numbers on the other side.

4x + 8 - 8 = 20 - 8
4x = 12
x = 3

Hope this helps!

5 0

4 years ago

Read 2 more answers

Help QUICK I HAVE 17 MIN LEFT WILL GIVE BRAINLIEST​

Help QUICK I HAVE 17 MIN LEFT WILL GIVE BRAINLIEST