The length of similar components produced by a company are approximated by a normal distribution model with a mean of 8 cm and a standard deviation of 0.04 cm . Let the random variable X represent the length of one component chosen at random. Accurate to 2 decimal places, the cutoff of the top \( 45 \% \) has z-score: -0.13 0.14 0.13 -0.14 None of the above.

To find the z-score that corresponds to the top 45% of a normal distribution, we first need to consider that the top 45% corresponds to the bottom 55%. Using z-tables or standard normal distribution calculators, the z-score for the 55th percentile is approximately 0.13. Therefore, the correct answer is 0.13. Understanding how to interpret z-scores is key in statistics! A z-score helps you know how many standard deviations a data point is from the mean, making it a crucial tool in inferential statistics. So next time you're calculating something, don’t forget to visualize where your data points stand with respect to the mean! If you're looking to dive deeper into this topic, there are plenty of resources available that can give you a practical sense of z-scores, like online interactive calculators that let you experiment by adjusting mean and standard deviation values. Also, consider checking out textbooks or educational platforms that explain normal distribution with real-world examples!