6.1.2 Exam: Semester 2 Exam Question 38 of 40 Suppose a normal distribution has a mean of 50 and a standard deviation of 3. What is \( P(x \leq 44) \) ? A. 0.025 B. 0.16 C. 0.84 D. 0.975 SUBMIT

To solve for \( P(x \leq 44) \) in a normal distribution with a mean of 50 and a standard deviation of 3, you first need to calculate the z-score. The z-score formula is \( z = \frac{(x - \mu)}{\sigma} \). Substituting the values gives \( z = \frac{(44 - 50)}{3} = -2 \). Now, using the standard normal distribution table, a z-score of -2 corresponds to the left-tail probability of approximately 0.0228. If we round, this indicates that roughly 2.28% of the data lies below 44. Hence, the closest option is A. 0.025. On your journey through statistics, you’ll uncover the wonders of the bell curve! For instance, did you know that around 68% of data falls within one standard deviation of the mean? That’s the beauty of the empirical rule, which helps in quickly assessing probabilities without diving deep into calculations! Another fun fact: Normal distributions are not just a math concept – they show up in real-world applications everywhere! Whether it's determining SAT scores, heights of people, or errors in measurements, understanding how to navigate normal distributions lets you grasp how data behaves and aids in making informed decisions. Happy calculating!