The primary political authority in society is the state.

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

Why is that surface area:Volume ratio so important? (About cells and microscopes)

OLga [1]

Answer:It affects the diffusion across a membrane

Explanation:

Since this is placed in the AP section, I assume it is AP Biology, which the syllabus puts emphasis on diffusion

The smaller the ratio is, the bigger the cell. SO, if the ratio is small enough, the molecule will not be able to diffuse through the membrane. Keep that in mind when you calculate different rations using the radius.

7 0

3 years ago

List 3 fertilizer delivery methods

Wittaler [7]

Broadcasting, placement, drilling :)

6 0

3 years ago

Explain your reasoning in words or by drawing. 1/3=4/12

AveGali [126]

As you can see both drawings take up the same amount of surface area and the same amount of surface area is colored. The one on the right has 12 spaces, while the one on the left only has 3.

3 0

3 years ago

In a preindustrial society much of the economy is involved in providing information and services. true or false

zloy xaker [14]

The statement is - False.

In the pre-industrial societies, the economy was far from being based on providing information and services. The economy was largely based on two things, agriculture and trade.

The agriculture was the basis and the dominant sector in the pre-industrial economy. The more agricultural products a nation had, the more it had to trade, thus becoming wealthy. This can easily be seen in the colonies that the European countries had in the pre-industrial period, where every inch of the land that was suitable for agriculture was used, and latter those products were shipped and traded in order to become wealthier.

7 0

3 years ago