In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 21.2 and a standard deviation of 6.4 . Complete parts (a) through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 20 . The probability of a student scoring less than 20 is Round to four decimal places as needed.)

To find the probability that a randomly selected high school student scored less than 20 on the reading portion of the test, we first convert the score to a z-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] Here, \( X = 20 \), \( \mu = 21.2 \), and \( \sigma = 6.4 \). Calculating the z-score: \[ z = \frac{(20 - 21.2)}{6.4} \approx \frac{-1.2}{6.4} \approx -0.1875 \] Now, we can look up the z-score in the standard normal distribution table or use a calculator to find the corresponding probability. A z-score of -0.1875 gives us a probability of approximately 0.4251. So, the probability that a randomly selected high school student has a score less than 20 is approximately **0.4251** when rounded to four decimal places. Now onto some additional fun facts! Many historical educators believed that standardized testing could predict future success based on performance in school subjects. Interestingly, these tests have evolved significantly over the decades, often leading to heated debates about fairness and accuracy in assessing student capabilities. In real-world applications, understanding how to interpret z-scores can be super helpful! For instance, if you work in education, you can better assess student performance trends and identify those who may need additional support, turning raw test scores into meaningful insights that can shape learning strategies.