Answer:
25.14% probability that his score is at least 582.5.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
![\mu = 506, \sigma = 114](https://tex.z-dn.net/?f=%5Cmu%20%3D%20506%2C%20%5Csigma%20%3D%20114)
If 1 of the men is randomly selected, find the probability that his score is at least 582.5.
This is 1 subtracted by the pvalue of Z when X = 582.5. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{582.5 - 506}{114}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B582.5%20-%20506%7D%7B114%7D)
![Z = 0.67](https://tex.z-dn.net/?f=Z%20%3D%200.67)
has a pvalue of 0.7486
1 - 0.7486 = 0.2514
25.14% probability that his score is at least 582.5.
9514 1404 393
Answer:
1000
Step-by-step explanation:
If the number of protesters per minute remains a constant, then you could write the proportion ...
p/12 = 177/2.1
Multiplying by 12 gives ...
p = 12(177/2.1) ≈ 1011.4
Here, minutes are given to 2 significant figures, and the initial count is given to 3 significant figures. The best you can hope for is that your estimate is good to 3 significant figures:
1010 protesters
It is probably sufficient to report the number to 2 significant figures*:
1000 protesters
_____
* Unfortunately, with a number like 1000, the only way you can tell it has 2 significant figures is to report it as 1.0×10³ or 10. hundreds. The trailing zeros are usually not considered significant.
Here is the explanation.
For the general complex number (a + bi), its conjugate is (a - bi).
By definition, i² = -1.
Evaluate (a + bi)*(a - bi) to obtain
(a + bi)*(a - bi) = a² - abi + abi - b²i²
= a² - b²*(-1)
= a² + b²
This means that multiplying a complex number by its conjugate yields a real number.
For this reason, it is customary to make the denominator of a complex rational expression into a real number, by multiplying the denominator by its conjugate.
Of course, the numerator should also be multiplied by the same conjugate.
Example:
Simplify (2 - 3i)/(1 + 4i) into the form a + bi.
The denominator is (1 + 4i) and its conjugate is (1 - 4i).
Multiply the denominator by its conjugate to obtain
(1 + 4i)*(1 - 4i) =1² + 4² = 17.
Also, multiply the numerator by the same conjugate to obtain
(2 - 3i)*(1 - 4i) = 2 - 8i - 3i + (3i)*(4i)
= 2 - 11i + 12*i²
= 2 - 11i - 12
= -10 - 11i
Therefore
(2 - 3i)/(1 + 4i) = -(10 + 11i)/17
I think it’s c but I’m not sure