Correct answer
$Z=frac(X−mu)sigmawhere(X)isthevalueofinterest(inthiscase,180ms),(mu)isthemean(150ms),and(sigma)isthestandarddeviation(30ms).Bysubstitutingthevaluesintotheformula,theZ−scorecanbecalculatedasfollows:Z=frac(180−150)30=1AZ−scoreof1indicatesthatthelatencyof180msisonestandarddeviationabovethemean.Tofindthepercentageoftimethelatencyexceeds180ms,theteamcanrefertothestandardnormaldistributiontable,whichshowsthatapproximately84.13100$ This analysis allows the team to understand how often the latency for the critical application exceeds acceptable thresholds, enabling them to take proactive measures to optimize performance. In contrast, the other options do not directly address the need to compare a specific value against a distribution. The mean absolute deviation focuses on the average distance of data points from the mean, which does not provide insights into the probability of exceeding a specific threshold. Confidence interval estimation is used to determine a range within which a population parameter lies, rather than assessing the likelihood of exceeding a particular value. Regression analysis is primarily concerned with relationships between variables rather than evaluating the distribution of a single variable. Thus, the Z-score calculation is the most appropriate method for this scenario.