The answer is X-2 ........
Let Xi be the random variable representing the number of units the first worker produces in day i.
Define X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
first worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, define random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the five days and define Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the difference between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDifferenceDistribution.html.
Now everything reduces to finding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .
Answer:
35/80
u want to find a number that is proportional to 35/80, then all u need is a number that is equivalent...another words, if it is proportional, it is an equivalent fraction to 35/80.
there can be several answers to this...such as 35/80 reduces to 7/16...so 7/16 is proportional....or if u multiply numerator and denominator by the same number, u will find a proportional number...
example :
35/80 * 2/2 = 70/160...this is proportional
35/80 * 3/3 = 105/240...this is proportional
35/80 * 4/4 = 140/320...this is also proportional
and so on....
so without giving us any answer choices, there can be many numbers to choose from
Let X be a random variable representing the mean gray scale of each pixel.
P(110 ≤ X ≤ 140) = P(X < 140) - P(X < 110) = P(z < (140 - 125)/15) - P(z < (110 - 125)/15) = P(z < 1) - P(z < -1) = P(z < 1) - [1 - P(z < 1)] = 2P(z < 1) - 1 = 2(0.84134) - 1 = 1.68268 - 1 = 0.68268
Number of pixels that have gray scale of between 110 and 140 = 0.68268 x 1000000 = 682680 = approximately 680,000