The weight on a bridge is estimated to have the uniform distribution between 3 and 5 tons. At 16 random times I record the vehicles on the bridge, and figure out the weight. I then compute the average of the 16 observations.

a) Define a random variable that is W = the weight on the bridge at observation i, i=1…16. Give the distribution, specify the parameters and give the expected value and variance.

b) Define another random variable =sample average of 16 observations of weight on the bridge. Give the distribution, specify the parameters and give the expected value and variance.

c) Find the probability that the sample average exceeds 4.5 tons.

d) Find the probability that the weight on the bridge at any given time exceeds 4.5 tons.

e) In each of the parts of question 10, show where you invoked the Central Limit Thm.