Final answer:
The question involves calculating the area under a normal curve to find probabilities using a z-table, scientific calculator functions like normalcdf, or inverse normal functions like invNorm for specific probabilities.
Step-by-step explanation:
The student's question is about calculating the area under the normal curve, which is a fundamental concept in statistics and is used to determine probabilities. The area under the curve to the left of a given z-score can be found using a z-table or technology such as a scientific calculator or computer software. For example, to find the area to the left that corresponds to a cumulative probability of 0.9, one would look up the z-score of approximately 1.28. Alternatively, commands such as normalcdf on a TI-83 or similar calculator can be used to calculate the area between two values with given mean and standard deviation, for example, normalcdf(65,1E99,63,5) will give the area to the right of a z-score of 65 in a distribution with mean 63 and standard deviation 5. To find z-scores corresponding to specific areas such as 0.975, invNorm(0.975,0,1) can be used, yielding a z-score of approximately 1.96 for the standard normal distribution.