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3 years ago

Discrete and continuous random variables

1 answer:

8 0

A continuous variable is a variable whose value is obtained by measuring. A random variable is avariable whose value is a numerical outcome of arandom phenomenon. A discrete random variable X has a countable number of possible values. Example: Let X represent the sum of two dice

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A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?

Brilliant_brown [7]

$x-\ number\ of\ dimes\\y-\ number\ of\ quarters\\\\ \left \{ {{x+y=250\ \ \ | x=250-y} \atop {0.1x+0.25y=39.25\ \ \ \ \ \ \ \ \ \ \ \ \ }} \right. \\\\ substitution\ method\\\\
0.1(250-y)+0.25y=39.25\\\\
25-0.1y+0.25y=39.25\\\\
25+0.15y=39.25\ \ \ \ | subtract\ 25\\\\0.15y=14.25\ \ \ \ | divide\ by\ 0.15\\\\y=95\\\\x=250-95=
155\\\\
There\ are\ 155\ dimes\ and\ 95\ quarters.$

8 0

3 years ago

∣∣x+34∣∣=−11, How do you solve this

VMariaS [17]

Answer:

The answer is No Solutions

Step-by-step explanation:

Since this is absolute value, we know the answer has to be positive, because distance has to be positive. We see it is negative, and that cannot be, so the answer is no solutions.

3 0

2 years ago

What is the greatest possible whole number remainder if you divide any number by 41

Dima020 [189]

40. Divide 81 by 41. 41 goes into 81 once with a remainder of 40

7 0

3 years ago

Read 2 more answers

Help! Need by 10:30 to turn in and I'm confused!

Alecsey [184]

Answer:

8 boxes of tissues

5 bags of cough drops

Step-by-step explanation:

You need to write a system of equations.

x = number of tissue boxes

y = number of cough drop bags

x (number of tissue boxes) + y (number of cough drop bags) = 13 (total number of tissues and cough drops combined.

So, your first equation is

x + y = 13

Then, you need to write the second equation.

(1.69 [cost of 1 tissue box] * [number of tissue boxes]) + (1.19 [cost of one bag of cough drops] * [number of cough drop bags] = 19.47 [total cost of tissues and cough drops]

That's a lot to read, so here's the equation simplified!

1.69x + 1.19y = 19.47

Now, you have two equations:

x + y = 13

1.69x + 1.19y = 19.47

I would solve with the substitution method.

the first equation can be changed to x = 13 - y by subtracting y from both sides.

Then, your two equations are:

x = 13 - y

1.69x + 1.19y = 19.47

Now, you can plug in that value of x into the second equation!

1.69(13 - y) + 1.19y = 19.47

21.97 - 1.69y + 1.19y = 19.47

subtract 21.97 from both sides

-1.69y + 1.19y = -2.5

Add the y values

-0.5y = -2.5

divide both sides by -0.5

so, y equals 5 bags of cough drops

now that you know what y equals, plug it back into your original equation to find x!

x + y = 13

plug in y

x + 5 = 13

x = 8

so, x = 8 boxes of tissues

Hope this helps! Let me know if you have any questions!

8 0

3 years ago

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted t

LekaFEV [45]

Answer:

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Step-by-step explanation:

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:

At the null hypothesis, we test if the mean is the same, that is:

$H_0: \mu = 59.5$

At the alternate hypothesis, we test that it is different, that is:

$H_a: \mu \neq 59.5$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

59.5 is tested at the null hypothesis:

This means that $\mu = 59.5$

After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.

This means that $n = 250, X = 59.2, \sigma = 1.9$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}$

$z = -2.5$

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.

Looking at the z-table, Z = -2.5 has a pvalue of 0.0062

2*0.0062 = 0.0124

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

5 0

2 years ago