91Ó°ÊÓ

We need to convert the given value into Z-scores using the formula \(Z=(X-μ)/σ\). Here, μ is the mean and σ is the standard deviation. For each of the four parts, we calculate the z-score:\na. \(Z = (69-80)/12 \approx -0.92\)\nb. \(Z = (73-80)/12 \approx -0.58\)\nc. \(Z = (101-80)/12 \approx 1.75\)\nd. \(Z = (87-80)/12 \approx 0.58\)

Once we have calculated the Z-score we can use the Z-table to find the probabilities. The Z-table shows the cumulative probabilities for the standard normal distribution.\na. For Z = -0.92, the table gives us the probability 0.1788, which is the cumulative probability from the left up to Z. But since we want to find the probability greater than 69, we take the complement: 1 - 0.1788 = 0.8212\nb. For Z = -0.58, the table gives us the cumulative probability 0.2810. Since we want less than 73, this is the probability we take.\nc. For Z = 1.75, the table gives us 0.9599. We want more than 101, so we take the complement: 1 - 0.9599 = 0.0401\nd. For Z = 0.58, the table gives us 0.7190. Since we want less than 87, this is the probability we take.