With reference to the Example 12, find the probability that \(I_{o} / I_{i}\) will take on a value between 7.0 and 7.5.

Data From Example 12

EXAMPLE 12 Maximum likelihood estimator: normal distribution variance Let X1, ..., Xn be a random sample of size n from a normal distribution with known mean. Obtain the maximum likelihood estimator of o. Solution The likelihood function is n L(ox1,...,xn) 1 -(xi-)/20 1 = e - 1 ()2/262 22 i=1 (22/2 The function ze cz has a maximum at z = b/c for z 20 when b and c are positive. Taking z = 1/02, b = n/2, and c=1(xi)/2, we obtain the maximum likelihood estimator o = -1(x; - )/n, when is known.