Final answer:
The question asks for the probabilities of certain salaries for full-time Ph.D. students, using the normal distribution and standard deviation. Calculating z-scores allows for finding these probabilities by referencing the standard normal distribution tables or using a calculator.
Step-by-step explanation:
The question involves finding probabilities from a normally distributed set of data, which in this case is the full-time Ph.D. student salaries. Given the average salary of $12,837 and a standard deviation of $1500, one can use z-scores to calculate various probabilities regarding the salaries. For example, the probability of a salary being above a certain amount, or between two amounts, can be computed by converting those salary amounts into z-scores and using the standard normal distribution tables.
To find a probability for a specific salary range using the z-score formula: z = (X - μ) / σ, where X is the salary of interest, μ is the mean salary, and σ is the standard deviation. Once the z-score is found, the standard normal distribution table or a calculator can be used to find the corresponding probability. Understanding the concept of normal distribution and z-scores is imperative for these calculations, especially for students involved in fields like statistics, economics, and other sciences that often deal with data analysis and interpretation.