Question
please help solve
(Derived Distributions) Points Possible: 10 Problems 1. A wall is constructed from 24 concrete blocks stacked as shown here The weight of a block is known to be normally distributed with a mean of 11.2 kg and a standard deviation of 0.688 kg. a) Determine the probability distribution for the total weight of the wall. Include the parameters b) The specifications indicate the wall should weigh less than 270 kg. What is the probability that the specification will not be met? It was determined the Gamma distribution was a better probability model of the weight of a slab. Now what is the probability that the specification will not be met? (An approximate probability is fine.) c) 2. The viscosity of a chemical compound is a random variable with probability density function xtn(1.5) The pressure is a random variable related to the viscosity by this relation: p 14.8 expected viscosity of the compound is 5.14. What is the expected pressure? 0.36x. The
Explanation / Answer
1)
X - weight of a block , which follows N(11.2,0.688^2)
a) Y = X1 + X2 + .. X24
Y follow N(11.2*24 , 24 * 0.688^2)
= N(268.8, 11.360256)
b) P(Y < 270)
= P(Z < (270 - 268.8)/sqrt(11.360256))
=P(Z< 0.3560304)
= 0.6391
2)p = 14.8 + 0.36 x
E(p) = E(14.8 + 0.36 x)
= 14.8 + 0.36 E(X)
= 14.8 + 0.36 *5.14 {note that exact E(X) comes out to be 4.9326 using pdf}
= 16.6504
