<span>The majority of the scores on the in test are between 85 to 115. This makes the mean 100 and the standard deviation 15. Anyone who scores above or below this range is ether more intelligent or less intelligent then the majority of participants in the test. Since Clara scored 118 she is smarter than most of the adults on this study.</span>
Answer:
C
Step-by-step explanation:
Because a parameter is regarding a whole population. The other options are samples of a population.
(i) The mean is
![\displaystyle E(X) = \sum_x x \, P(X = x) \\\\ E(X) = 1\cdot0.175 + 2\cdot0.315 + 3\cdot0.211 + 4\cdot0.092 + 5\cdot0.207 \\\\ \boxed{E(X) = 2.839}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20E%28X%29%20%3D%20%5Csum_x%20x%20%5C%2C%20P%28X%20%3D%20x%29%20%5C%5C%5C%5C%20E%28X%29%20%3D%201%5Ccdot0.175%20%2B%202%5Ccdot0.315%20%2B%203%5Ccdot0.211%20%2B%204%5Ccdot0.092%20%2B%205%5Ccdot0.207%20%5C%5C%5C%5C%20%5Cboxed%7BE%28X%29%20%3D%202.839%7D)
The variance is
![V(X) = E((X - E(X))^2) = E(X^2) - E(X)^2](https://tex.z-dn.net/?f=V%28X%29%20%3D%20E%28%28X%20-%20E%28X%29%29%5E2%29%20%3D%20E%28X%5E2%29%20-%20E%28X%29%5E2)
Compute the second moment
:
![\displaystyle E(X^2) = \sum_x x^2 \, P(X = x) \\\\ E(X) = 1^2\cdot0.175 + 2^2\cdot0.315 + 3^2\times0.211 + 4^2\times0.092 + 5^2\times0.207 \\\\ E(X^2) = 9.997](https://tex.z-dn.net/?f=%5Cdisplaystyle%20E%28X%5E2%29%20%3D%20%5Csum_x%20x%5E2%20%5C%2C%20P%28X%20%3D%20x%29%20%5C%5C%5C%5C%20E%28X%29%20%3D%201%5E2%5Ccdot0.175%20%2B%202%5E2%5Ccdot0.315%20%2B%203%5E2%5Ctimes0.211%20%2B%204%5E2%5Ctimes0.092%20%2B%205%5E2%5Ctimes0.207%20%5C%5C%5C%5C%20E%28X%5E2%29%20%3D%209.997)
Then the variance is
![\boxed{V(X) \approx 1.9171}](https://tex.z-dn.net/?f=%5Cboxed%7BV%28X%29%20%5Capprox%201.9171%7D)
(ii) For a random variable
, where
are constants, we have
![E(Z) = E(aX+b) = E(aX) + E(b) = a E(X) + b](https://tex.z-dn.net/?f=E%28Z%29%20%3D%20E%28aX%2Bb%29%20%3D%20E%28aX%29%20%2B%20E%28b%29%20%3D%20a%20E%28X%29%20%2B%20b)
and
![V(Z) = E((aX+b)^2) - E(aX+b)^2 \\\\ V(Z) = E(a^2 X^2 + 2ab X + b^2) - (a E(X) + b)^2 \\\\ V(Z) = a^2 (E(X^2) - E(X)^2) \\\\ V(Z) = a^2 V(X)](https://tex.z-dn.net/?f=V%28Z%29%20%3D%20E%28%28aX%2Bb%29%5E2%29%20-%20E%28aX%2Bb%29%5E2%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20E%28a%5E2%20X%5E2%20%2B%202ab%20X%20%2B%20b%5E2%29%20-%20%28a%20E%28X%29%20%2B%20b%29%5E2%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20a%5E2%20%28E%28X%5E2%29%20-%20E%28X%29%5E2%29%20%5C%5C%5C%5C%20V%28Z%29%20%3D%20a%5E2%20V%28X%29)
Then for
, we have
![E(Y) = \dfrac12 E(X) + \dfrac32 \\\\ \boxed{E(Y) = 2.918}](https://tex.z-dn.net/?f=E%28Y%29%20%3D%20%5Cdfrac12%20E%28X%29%20%2B%20%5Cdfrac32%20%5C%5C%5C%5C%20%5Cboxed%7BE%28Y%29%20%3D%202.918%7D)
![E(Y^2) = E\left(\left(\dfrac{X+3}2\right)^2\right) = \dfrac14 E(X^2) + \dfrac32 E(X) + \dfrac94 \\\\ \boxed{E(Y^2) \approx 9.0028}](https://tex.z-dn.net/?f=E%28Y%5E2%29%20%3D%20E%5Cleft%28%5Cleft%28%5Cdfrac%7BX%2B3%7D2%5Cright%29%5E2%5Cright%29%20%3D%20%5Cdfrac14%20E%28X%5E2%29%20%2B%20%5Cdfrac32%20E%28X%29%20%2B%20%5Cdfrac94%20%5C%5C%5C%5C%20%5Cboxed%7BE%28Y%5E2%29%20%5Capprox%209.0028%7D)
Answer:
2 hundredth
Step-by-step explanation:
the number directly after a point is called a tenth and the next a hundredth and so on
pls mark brainliest
Answer:
X = 13
Step-by-step explanation:
x + x + 3 + x - 2 + 3x + 9 - 1 = 87
6x + 9 = 87
6x = 87 - 9
6x = 78
x = 78/6
x = 13