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OleMash [197]
3 years ago
12

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag fo

llows the continuous uniform distribution with low and high filling weights of 10 pounds and 12 pounds, respectively. a. Calculate the expected value and the standard deviation of this distribution. (Do not round intermediate calculations. Round your "Standard deviation" answer to 4 decimal places.) Expected value Standard deviation b. Find the probability that the weight of a randomly selected bag is no more than 11 pounds. (Round your answer to 2 decimal places.) Probability c. Find the probability that the weight of a randomly selected bag is at least 10.5 pounds. (Round your answer to 2 decimal places.)
Mathematics
1 answer:
defon3 years ago
3 0

Answer:

a) The expected value is given by:

E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11

The variance is given by:

Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333

And the standard deviation is just the square root of the variance and we got:

Sd(x) = \sqrt{0.3333}= 0.5774

b) P(X

And we can use the cumulative distribution function given by:

F(x) = \frac{x-a}{b-a}, a \leq x \leq b

And using this function we got:

P(X

c) P(X>10.5)

And using the complement rule and the cumulative distribution function we got:

P(X>10.5)= 1-P(X

Step-by-step explanation:

For this case we define the random variable X=quantity put in each bag , and we know that the distribution for X is given by:

X \sim Unif (a= 10, b =12)

Part a

The expected value is given by:

E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11

The variance is given by:

Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333

And the standard deviation is just the square root of the variance and we got:

Sd(x) = \sqrt{0.3333}= 0.5774

Part b

For this case we want this probability:

P(X

And we can use the cumulative distribution function given by:

F(x) = \frac{x-a}{b-a}, a \leq x \leq b

And using this function we got:

P(X

Part c

For this case we want this probability:

P(X>10.5)

And using the complement rule and the cumulative distribution function we got:

P(X>10.5)= 1-P(X

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Write the polynomial of least degree with roots -2, 0, 1.
joja [24]
So since -2, 0, 1 are the roots:

Therefore  x = -2,  x = 0 ,  x = 1

Implies that:

x = 2        x - 2 = 0

x = 0          x = 0

x = 1        x - 1 = 0


Therefore    (x - 2)x(x - 1) = 0

(x - 2)(x - 1) =   x(x - 1) - 2(x - 1) =  x² - x - 2x + 2 = x² - 3x + 2

(x - 2)x(x - 1) = 0

(x - 2)(x - 1)x = 0

(x² - 3x + 2)x = 0

x*x² - x*3x + x*2 = 0

x³ - 3x² + 2x = 0

This is the polynomial with the least degree, because it possible for another polynomial with higher power to still have the same root.

 x³ - 3x² + 2x = 0    is the polynomial.

I hope this helps.
6 0
3 years ago
I need help anyone,<br> I will thank u a lot
Margarita [4]

Answer:

18=1/12

Step-by-step explanation:

you take both fractions and multiply them to get 1/12

6 0
3 years ago
Read 2 more answers
-6x+6y=6<br> -6x+3y=-12<br> How do you solve this problem?
sergij07 [2.7K]

Answer:

That's called system of equations. it is like adding and subtracting.

Step-by-step explanation:

first you want to find x or y. i will choose x. in order to do that you need to put one, ill do the first one but you can do first or second, and change it to negative (-6x+6y=6) or -(-6x+6y=6), changing it to 6x - 6y = -6. then the two x's will be cancled since 6-6 is 0. now you add 6y and 3y, and 6 with -12. get your answer, and do the same thing to y, too. sorry if its a bit confusing, took me a while to learn it too. this is highschool stuff so thats why you will although im im middle too!

3 0
3 years ago
Part 1: How's the weather? A. Investigate the weather forecast in your city. Record the high and low temperatures that are forec
victus00 [196]

Using the mean concept, it is found that:

1. The mean change in the forecasted high temperatures is of -0.33ºC.

2. The mean change in the forecasted low temperatures is of 0.5ºC.

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

The mean of data-set is given by the <u>sum of all observations divided by the number of observations.</u>

Item 1:

The changes in the high temperature are: 2, 1, -1, -1, -1, -2

Thus:

M = \frac{2 + 1 - 1 - 1 - 1 - 2}{6} = -0.33

The mean change in the forecasted high temperatures is of -0.33ºC.

Item 2:

The changes in the low temperature are: 2, -2, 2, 1, 0, 0.

M = \frac{2 - 2 + 2 + 1 + 0 + 0}{6} = 0.5

The mean change in the forecasted low temperatures is of 0.5ºC.

A similar problem is given at brainly.com/question/24754716

3 0
2 years ago
How does slope affect a linear graph??
Alja [10]

Answer:

With positive slope the line moves upward when going from left to right. With negative slope the line moves down when going from left to right.

hope this helps

Step-by-step explanation:

7 0
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