Final answer:
This question involves finding specific values related to the chi-square distribution, such as probability values and critical chi-square values for a given degree of freedom, and rounding them to the required decimal places.
Step-by-step explanation:
The student's question is related to the chi-square distribution and involves calculations to find certain probability values associated with this distribution. To solve these types of problems, students typically use statistical tools or tables that provide values associated with the chi-square distribution.
For part (a), the calculation might involve finding a value such as P(χ^2 > k) for a certain degree of freedom and for part (b), finding a chi-square value that corresponds to a certain percentile, e.g., P(χ^2 < k) for a specific degree of freedom. It is important to round the expected frequency and any statistical values to the appropriate number of decimal places as indicated by the question or statistical convention.