How do you do this? I have no idea

A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red. She estimates th

sergij07 [2.7K]

Answer:

(a) The mean or expected value of X is 2.2.

(b) The standard deviation of X is 1.3.

Step-by-step explanation:

Let X = number of times the traffic light is red when a commuter passes through the traffic lights.

The probability distribution of X id provided.

The formula to compute the mean or expected value of X is:

$\mu=E(X)=\sum x.P(X=x)$

The formula to compute the standard deviation of X is:

$\sigma=\sqrt{E(X^{2})-(E(X))^{2}}$

The formula of E (X²) is:

$E(X^{2})=\sum x^{2}.P(X=x)$

(a)

Compute the expected value of X as follows:

$E(X)=\sum x.P(X=x)\\=(0\times0.06)+(1\times0.25)+(2\times0.35)+(3\times0.15)+(4\times0.13)+(5\times0.06)\\=2.22\\\approx2.2$

Thus, the mean or expected value of X is 2.2.

(b)

Compute the value of E (X²) as follows:

$E(X^{2})=\sum x^{2}.P(X=x)\\=(0^{2}\times0.06)+(1^{2}\times0.25)+(2^{2}\times0.35)+(3^{2}\times0.15)+(4^{2}\times0.13)+(5^{2}\times0.06)\\=6.58$

Compute the standard deviation of X as follows:

$\sigma=\sqrt{E(X^{2})-(E(X))^{2}}\\=\sqrt{6.58-(2.22)^{2}}\\=\sqrt{1.6516}\\=1.285\\\approx1.3$

Thus, the standard deviation of X is 1.3.

4 0

3 years ago

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HELP PLEASE What is the area of the kite below?

Kryger [21]

Answer:

Area = 33 inches squared

Step-by-step explanation:

The formula for the area of a kite is:

Area = ½ × (d)1 × (d)2

To find the first diagonal (d1):

d1 = 7 in + 4 in = 11 in

To find the second diagonal (d2):

The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.

d2 = 3 in + 3 in = 6 in

Now we can plug the diagonals into the area formula.

Area = ½ × 11 × 6 = 33 inches squared

6 0

1 year ago

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Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil. What would one pencil and one

vladimir2022 [97]

It is given in the question that

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil.

Let the cost of pencil is $ x .

Therefore cost of pen is

$$(x+0.40)$

According to the question

$12(x+0.40)+20x =16$

Distributing 12 and combining like terms, we will get

$12x+4.8+20x=16\\32x = 11.2\\x = 0.35$

Therefore cost of pencil is $0.35 and cost of pen is

$0.35+0.40=0.75$

3 0

3 years ago

How do you find the variable when it’s on both sides of the equation

ASHA 777 [7]

If, for example, you had x on one side and x on the other, then subtracting x from both sides "disappears" x. If no other power of x shows up on either side, then your equation either has no solution or is always true.

3 0

3 years ago

HELP ASAP! BEING TIMED!

Sloan [31]

Answer:

7

Step-by-step explanation:

that what i thank it is

6 0

2 years ago

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