A computational biologist models gene expression across 5 cell cultures. The expression levels of a key gene are 120, 145, 130, 155, and 160 units. She applies a linear transformation $ y = ax + b $ to normalize data such that the lowest becomes 0 and the highest becomes 100. What is the normalized value for the highest expression culture?

["What Shifting Gene Expression Data Tells Us—And How Normalization Reveals Hidden Patterns", "In the rapidly evolving landscape of biomedical research, one question is increasingly shaping discussions among scientists and clinicians: How do we accurately interpret and compare gene expression across diverse cell cultures? A direct look at five distinct cell lines—showing expression levels of 120, 145, 130, 155, and 160 units—reveals nuances critical for understanding cellular behavior. When transformed via a linear equation to scale values from 0 to 100, the highest reading emerges not just as a number, but as a meaningful benchmark in broader biological analysis. This shift in presentation holds growing significance in research reports, diagnostics, and educational content, making precision both a scientific and a communicative necessity.", "---", "### Why This Data Model Matters in Modern Research", "The measurement of gene expression levels across multiple cell cultures reflects a trend toward comparative genomics—a cornerstone of contemporary biology. Researchers analyze how key genes behave under differing conditions, treatments, or environmental cues. In one recent study, five cell cultures displayed varying expression patterns, raising the question: how do we fairly compare these signals? By applying a standardized normalization technique, scientists convert raw numbers into comparable scales. This shift supports clearer interpretation, better collaboration, and stronger data-driven conclusions—especially when exploring disease mechanisms or drug sensitivity. It’s a subtle but powerful step in bridging lab results with real-world insight.", "---", "### How Normalization Transforms Raw Data into Meaning", "At the heart of this shift lies a fundamental transformation: converting raw gene expression units into a normalized scale where the lowest value maps to 0 and the highest to 100. For the highest reading—160 units in this case—this process ensures fair representation independent of measurement scale. Using a linear function $ y = ax + b $, the transformation is founded on two anchors: the minimum and maximum values in the dataset. By plugging in these extremes, we derive precise coefficients that map every data point along a consistent continuum. This method preserves relative differences, making it reliable for both scientific analysis and educational explanation.", "To calculate the normalized value for the highest expression, the formula uses: \n- Minimum = 120, Maximum = 160 \n- Slope $ a = \frac{100 - 0}{160 - 120} = \frac{100}{40} = 2.5 $ \n- Intercept $ b = 0 $ (since 120 maps directly to 0)", "Thus, \n$ y = 2.5 \ imes (160 - 120) = 2.5 \ imes 40 = 100 $", "The normalized value for the highest expression culture is therefore exactly 100.", "---", "### What This Normalized Peak Reveals Beyond the Number", "Normalizing so precisely does more than scale data—it enables clarity. A normalized peak at 100 signals a strong"]