Answer:
a) X has a mean of 25 and a variance of 8.
b) The probability that the total weight X is between 22 and 28 oz is 0.711.
Step-by-step explanation:
We have to calculate the mean and variance of a sum of random normal variables.
We can apply the rule for mean and variance for sum of independent variables:
![X=L+M\\\\E(X)=E(L+M)=E(L)+E(M)\\\\V(X)=V(L+M)=V(L)+V(M)-2CoV(L,M)=V(L)+V(M)](https://tex.z-dn.net/?f=X%3DL%2BM%5C%5C%5C%5CE%28X%29%3DE%28L%2BM%29%3DE%28L%29%2BE%28M%29%5C%5C%5C%5CV%28X%29%3DV%28L%2BM%29%3DV%28L%29%2BV%28M%29-2CoV%28L%2CM%29%3DV%28L%29%2BV%28M%29)
Then, the mean and variance of X is:
![E(X)=E(L)+E(M)=15+10=25\\\\\\V(X)=V(L)+V(M)=2^2+2^2=4+4=8\\\\\sigma_x=\sqrt{V(X)}=\sqrt{8}\approx2.83](https://tex.z-dn.net/?f=E%28X%29%3DE%28L%29%2BE%28M%29%3D15%2B10%3D25%5C%5C%5C%5C%5C%5CV%28X%29%3DV%28L%29%2BV%28M%29%3D2%5E2%2B2%5E2%3D4%2B4%3D8%5C%5C%5C%5C%5Csigma_x%3D%5Csqrt%7BV%28X%29%7D%3D%5Csqrt%7B8%7D%5Capprox2.83)
We can calculate the probability that X is between 22 and 28 as:
![z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{22-25}{2.83}=\dfrac{-3}{2.83}=-1.06\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{28-25}{2.83}=\dfrac{3}{2.83}=1.06\\\\\\P(22](https://tex.z-dn.net/?f=z_1%3D%5Cdfrac%7BX_1-%5Cmu%7D%7B%5Csigma%7D%3D%5Cdfrac%7B22-25%7D%7B2.83%7D%3D%5Cdfrac%7B-3%7D%7B2.83%7D%3D-1.06%5C%5C%5C%5C%5C%5Cz_2%3D%5Cdfrac%7BX_2-%5Cmu%7D%7B%5Csigma%7D%3D%5Cdfrac%7B28-25%7D%7B2.83%7D%3D%5Cdfrac%7B3%7D%7B2.83%7D%3D1.06%5C%5C%5C%5C%5C%5CP%2822%3CX%3C28%29%3DP%28z%3C1.06%29-P%28z%3C-1.06%29%5C%5C%5C%5CP%2822%3CX%3C28%29%3D0.855-0.145%3D0.711)
Answer:
C=12
Step-by-step explanation:
2x12=24
3x12=36
5x12=60
18+17 or 18+ (8+9)
I hope this helps...
Answer:
J. 500 inches
Step-by-step explanation:
There are 4 sides to a square so, to find the measure of each of the lengths, u have to... 2,000 ÷ 4 = 500 inches each side length