Calculating Probabilities in Normal Distribution The problem involves a normal distribution with a mean of 70 and standard deviation of 5. For scores less than 65, the Z-score is -1, yielding a probability of approximately 0.1587; multiplying by the total number (1000 students) gives about 159 students scoring below this mark. Similarly, for scores above 75 (Z = +1), the same probability applies due to symmetry in normal distributions—resulting again in around 159 students.
Finding Students Between Two Scores Using Symmetry To find how many scored between marks like [65-75], calculate probabilities using Z-scores (-1 to +1). The area under this range equals twice P(0 < Z < +1), which sums up as ~68% or specifically ~682 outta thousand cases fitting criteria!