Final answer:
The question involves calculating areas under the standard normal curve to find probabilities, which is done through the use of z-scores and a z-table. This method is pivotal in statistics and various applications across fields to interpret data and make inferences.
Step-by-step explanation:
The student's question pertains to finding the eareas under the standard normal curve which is a key aspect of working with normal distributions in statistics. The area under the normal curve is indicative of probability, and to find it one must use z-scores which can be looked up in a z-table or calculated using statistical tools. The process involves standardizing a value by subtracting the mean and dividing by the standard deviation to get the z-score, and then interpreting these scores using the z-table which provides the area to the left of a given z-score. The area under the curve for specific intervals can be used to answer various statistical questions, such as probabilities of obtaining certain values, percentile ranks and may be applied to a range of fields, from psychology to quality control.
For example, to find the z-score corresponding to the 90th percentile, one would look for the z-value that has 0.90 of the area under the curve to its left. The respective area under the curve to the right of the z-score or between z-scores can be found by simple arithmetic manipulations such as subtraction from the total area (which is 1 for the normal distribution).
When working with normal distributions, it's essential to understand the concept of z-scores and the z-table. These concepts are used broadly across various industries and research fields to describe and infer statistical data. This framework allows comparisons across different datasets and aids in decision making based on statistical probabilities.