Solve the equation 5/7 (x-9)=25

Suppose the ice Q scores in one region are normally distributed within a standard deviation of 13. Suppose also that exactly 51%

elena-14-01-66 [18.8K]

Answer:

$z=-0.025$

And if we solve for $\mu$ we got

$\mu=100 +0.025*13=100.325$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,13)$

Where $\mu=?$ and $\sigma=13$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

For this case we know these conditions:

$P(X>100)=0.51$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.49 of the area on the left and 0.51 of the area on the right it's z=-0.025. On this case P(Z<-0.025)=0.49 and P(z>-0.025)=0.51

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.025$

And if we solve for $\mu$ we got

$\mu=100 +0.025*13=100.325$

8 0

3 years ago

Write 6×6×6×6×4×4 in expontential form

densk [106]

Simplify the equation

6x6x6 can be written as 6³

And 4x4 can be written as 4²

So in conclusion

6³×4²

7 0

3 years ago

A computer chess game and a human chess champion are evenly matched. They play ten games. Find probabilities for the following e

AleksAgata [21]

Answer:

(a) The probability that each of them win five games is 0.2461.

(b) The probability that the computer wins seven games is 0.1172.

(c) The probability that the human wins at least 7 games is 0.1711.

Step-by-step explanation:

Let the random variable X = the human wins a chess game.

The probability that the human wins a game is, P (X) = p = 0.50.

The number of games played by the computer and the human is, n = 10.

The random variable $X\sim Bin(n = 10,p=0.50)$

The probability distribution of the Binomial random variable X is:

$P (X=x)={n\choose x}p^{x}(1-p)^{n-x}={10\choose x}(0.50)^{x}(1-0.50)^{10-x}$

(a)

If both the computer and the human wins five games each then the probability of the human winning 5 games is:

$P (X=5)={10\choose 5}(0.50)^{5}(1-0.50)^{10-5}\\=252\times 0.03125\times0.03125\\=0.246094\\\approx 0.2461$

Thus, the probability that each of them win five games is 0.2461.

(b)

If the computer wins 7 games then the number of games won by the human is, 10 - 7 = 3.

P (Computer winning 7 games) = P (Human winning 3 games)

The probability that the human wins 3 games is:

$P (X=3)={10\choose 3}(0.50)^{3}(1-0.50)^{10-3}\\=120\times 0.125\times0.0078125\\=0.1171875\\\approx 0.1172$

Thus, the probability that the computer wins seven games is 0.1172.

(c)

Compute the probability that the human wins at least 7 games as follows:

$P(X\geq 7)=P(X=7)+P(X=8)+P(X=9)+P(X=10)\\={10\choose 7}(0.50)^{7}(1-0.50)^{10-7}+{10\choose 8}(0.50)^{8}(1-0.50)^{10-8}\\+{10\choose 9}(0.50)^{9}(1-0.50)^{10-9}+{10\choose 10}(0.50)^{10}(1-0.50)^{10-10}\\=0.1172+0.044+0.009+0.0009\\=0.1711$

Thus, the probability that the human wins at least 7 games is 0.1711.

5 0

4 years ago

Express using algebra. Jane is 3 years older than Mary, and Mary is twice as old as Kay. If Kay is x years old, how old is Jane?

krok68 [10]

Kay = x

Mary is twice as old as Kay
⇒ Mary = 2x

Jane is 3 years older than Mary
⇒ Jane = 2x + 3

Answer: 2x + 3

5 0

4 years ago

Identify the y-intercept of g(x). f(x) = x2 – 4 g(x) = f(x) – 5

Evgesh-ka [11]

- 5 because that's where the line crosses the y axis on a graph

8 0

4 years ago