3.4 The scores on a battery of three tests are given by z’ = (z1,z2,z3). Suppose 100 people are tested and the results are summarized from observations z1, . . . ,z100 by where z and V are the sample mean vector and unnormed sample covariance matrix. Suppose L(Z|θ, ) = N(θ, ). Assume a diffuse prior for θ and and find, assuming > 0, the predictive distribution for a new observation y’ = (y1,y2,y3), P{65 ≤ y1 ≤ 70|z1,z2, . . . ,z100}.