The ratio of red jellybeans to purple jellybeans is 9:5. What fraction of the jellybeans are red?

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 and explain explain !!!!!!!!!!

tigry1 [53]

Answer:

$x=-1\text{ or }x=11$

Step-by-step explanation:

For $a=|b|$ , we have two cases:

$\begin{cases}a=b,\\a=-b\end{cases}$

Therefore, for $18=|15-3x|$ , we have the following cases:

$\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}$

Solving, we have:

$\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}$ .

Therefore,

$\implies \boxed{x=-1\text{ or }x=11}$

3 0

3 years ago

What is a million times all the numbers in the world

kozerog [31]

Well, there isn’t really an end for numbers...

However; The biggest number referred to regularly is a googolplex (10googol), which works out as 1010^100. That isn’t the end to numbers but it is a huge one. We will replace that with ‘all the numbers in the world’.

106 is the exponent equivalent to 1 million

So your question would be:
106 x 1010^100 =

However I don’t believe there is a calculator that large.

7 0

3 years ago

HELP ASAP stats and probs

natka813 [3]

Answer:

Step-by-step explanation:

7 0

2 years ago

10. Look at the diagram. Which of the following is a pair of vertical angles?

MArishka [77]

Answer:

1 option is correct

Step-by-step explanation:

Angle AOB and DOC is vertically opposite angle

7 0

3 years ago

Read 2 more answers