What is one-half divided by one-eight?

In a bag of marbles you have three green, two yellow, six blue, and nine red marbles. What is the probability of picking a red m

guajiro [1.7K]

$|\Omega|=3+2+6+9=20-a\ number\ of\ all\ marables\\\\|R|=9-a\ number\ of\ red\ marables\\\\\boxed{P(R)=\dfrac{9}{20}}$

3 0

3 years ago

The process standard deviation is 0.27, and the process control is set at plus or minus one standard deviation. Units with weigh

mr_godi [17]

Answer:

a) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

b) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

c) For this case the advantage is that we have less items that will be classified as defective

Step-by-step explanation:

Assuming this complete question: "Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situation.

Part a

The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects."

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 weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,0.15)$

Where $\mu=10$ and $\sigma=0.15$

We can calculate the probability of being defective like this:

$P(X$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And if we replace we got:

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

Part b

Through process design improvements, the process standard deviation can be reduced to .05. Assume the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects.

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

Part c What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

For this case the advantage is that we have less items that will be classified as defective

5 0

2 years ago

If each 6 in. On the scale drawing below equals 3 feet, what is the actual area of the shape in square units?

Liono4ka [1.6K]

Answer:

32 ft²

Step-by-step explanation:

Assuming the diagram attached below similar to the one required to complete the question below.

From the diagram,

Actaul Area of a parallelogram (A) = Actual Base(b)× actual heigth(h)

A = bh.......................... Equation 1

From the question,

If each 6 in on the scale drawing equals 3 feet

Given:

base on the scale drawing = 8 in.

Actual base(b) = (8×3)/6 = 4 feet.

Height on the scale drawing = 16 in

Actual height(h) = (16×3)/6 = 8 feet.

Substitute these values into equation 1

A = 4×8

A = 32 ft²

Hence the actual area of the shape is 32 ft²

4 0

2 years ago

Could you please help with this question for domain, range, and end behavior? I started it, but I think I'm doing it wrong.

Tanzania [10]

It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write

$\{x\in\re\mathbb{R}\}$

and in interval notation,

$(-\infty,\infty)$

The <em>range</em>, on the other hand, is the set of all possible <em>outputs</em> of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that

$f(x)\leq3$ ,

in set notation:

$\{f(x)\in\mathbb{R}\ |\ f(x)\leq3\}$

(this just means "f(x) is a real number less than or equal to 3")

and in interval notation:

$(-\infty,3]$

8 0

3 years ago

PLEASE HELP!!

sp2606 [1]

Standard form is just putting (in this case) variables in alphabetical order. First we simplify- 2x+4=4y would become 1/2x+1=y. This is already in standard form, as numbers w/o variables come at the end. simplifying the next one is more tricky. first you get a variable/number alone-
9-2x-2y=4x+3
9-2y=6x+3
6-2y=6x
1-1/3y=x
1=x+1/3y
3=x+y
x+y=3
sorry if I was wrong and not of any help, But I do believe this is correct.

5 0

3 years ago

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