Order from least to greatest 1.312, 1 3/8, -1 3/10, -1.33

Svet_ta [14]

The mean for the total cost of the two items is 82. The standard deviation of the total cost of the two items is 14.14214. The probability of finding two random items at this auction with a total price of less than $80 is 0.44377.

<h3>What is a random variable?</h3>

A random variable is a variable with an undetermined value that gives values to each of the results of a statistical experiment.

From the parameters given:

Let us assume that X represents the random variable that connotes the price of the item during the large auction.

Given that:

X is normally distributed with a mean of $41 and
A standard deviation of $10

X $\sim$ N(μ, σ²)

X $\sim$ N(41, 10²)

Suppose we made an assumption that Y should denote the total cost of items:

i.e.

Y = X₁ + X₂

Here;

$\mathbf{X_i \sim N(41, 10^2)} \\ \\ \mathbf{E(Y) = E(X_1+X_2) } \\ \\ \mathbf{E(Y) = 41 + 41 } \\ \\ \mathbf{E(Y) = 82}$

The variance of (Y) is:

$\mathbf{Var (Y) = Var(X_1+X_2) = Var (X_1) + Var(X_2) } \\ \\\mathbf{= 10^2+ 10^2} \\ \\ \mathbf{=200}$

$\mathbf{Standard \ deviation \ SD (Y) = \sqrt{200} }$

= 14.14214

The probability of finding the two random items at the auction with a total price of less than $80 can be computed as:

P(Y < 80)

Since the data is normally distributed,

$\mathbf{=P\Big(Z < \dfrac{x -\mu}{\sigma}\Big)}$

$\mathbf{=P\Big(Z < \dfrac{80 -82}{14.14214}\Big)}$

$\mathbf{=P\Big(Z < -0.1414213\Big)}$

Recall that:

P(Z < -z) = P(Z > z)

Hence;

= P (Z > 0.1414213)

= 1 - P(Z ≤ 0.1414213)

From the Z tables, the value of Z at 0.1414213 is 0.55623;

= 1 - 0.55623

= 0.44377

Therefore, we can conclude that the probability of finding two random items at this auction with a total price of less than $80 is 0.44377.

Learn more about random variables in probability here:

brainly.com/question/15246027

7 0

2 years ago

TIPLE CHOICE. Choose the one alternative that

Akimi4 [234]

Answer is A ...............................

6 0

3 years ago

Read 2 more answers

1. Write the recursive formula and the explicit formula for the sequence {3,6,12,24,48,...}. Show all work.

Evgesh-ka [11]

1. The given sequence is a geometric sequence.

The nth term of a geometric sequence is given by

$a_{n} = a_{1} r^{n-1}$

where $a_{n}$ is the nth term of the sequence,

$a_{1}$ is the first term of the sequence and

r is the common ratio.

In the given sequence,

a₁ = 3 and r = 2

∴ aₙ = 3(2ⁿ⁻¹)

2. All geometric sequences are discrete form of exponential functions.

A geometric sequence is given by

aₙ = a₀ rⁿ , where n is a discrete value, in other words, a counting integer.

If the discrete value, n is replaced by a continuous variable, x , the resulting function is exponential in nature.

3. Here, the given function is f(x) = 3(1.06 x) + 2.

We see that, f(x) increases with increase in x.

Let us assume x to be the amount of gold in grams and f(x) to be the price of gold.

The cost of gold is directly proportional to the amount of gold bought and there is a flat tax collected, which is 2 bucks.

4. Constant rate of change : When a quantity changes uniformly over the another quantity, it is said to constant change over the other. For example, when a car covers a distance of 50 km every hour, the car is said to have a constant speed, which is rate of change of distance.

Average rate of change : It is the average rate at which one quantity is changing with respect to another. Suppose let us take the car to be covering a distance of 50 km in the first hour and 60 km in the second hour. Here, the rate of change in first hour is 50 kmph, where as in the second is 60 kmph. The average rate of change is 55 kmph.

5. Average rate of change is the slope of the function.

Here the function is g(x)=6x-6

If y = mx+c, the slope is m.

Here, the function is also of the same form, where m =6 and c = -6.

So, the slope of the equation is 6.

Average rate of change is 6 in the interval, 0≤x≤3

4 0

3 years ago

To reduce the likelihood of back pain, use a safe ______ technique. adjust your chair’s lumbar support. avoid awkward twisting p

Ivanshal [37]

I believe the answer is: Lifting

There are several things that must be followed to adhere to a safe lifting technique. The first one is to make sure that you have a proper grip on the object that you lift. The second one is to not bend or twist the waist during the lifting motion, your back and waist should always be straight. The last one is to keep your legs shoulders-width apart.

7 0

3 years ago

Read 2 more answers

Assume that your classmate suggested that both graphs represent constant opportunity costs because movement from combinations A

sveta [45]

Answer:

The movement of the combinations, explained by your classmate, is presented in an equal way, which does not represent an opportunity cost. In order to be able to perceive a constant opportunity cost, the combinations should present different values, and the choice of one of them, would cause the loss of opportunity to submit to the results that would be obtained with the choice of the others. However, as all combinations are the same, choosing any one would give the same results.

Explanation:

A constant opportunity cost refers to the presentation of elements in a business that would happen differently from each other and that would present different profitable results in a constant and extended way, showing the value and benefits that each one has individually.

7 0

3 years ago