Final answer:
The student's question requires finding the value of k to ensure function continuity or to find a specific percentile in a continuous probability distribution, and it involves understanding the definition of continuity in mathematics and calculating z-scores in statistics.
Step-by-step explanation:
The student's question involves finding the value of k such that a function f is continuous at every point. To determine k for the continuity of the function, you need to use the definition of continuity.
A function is continuous at a point if the limit from the left, the limit from the right, and the value of the function at that point all exist and are equal.
For percentile calculations in statistics, the 90th percentile is found by determining the score above which 10 percent of the scores lie. Using a standard normal distribution, this involves finding the z-score that corresponds to the cumulative area of 0.90.
A continuous probability density function, denoted by f(x), represents probabilities in terms of areas under the curve between specific bounds on the x-axis.
Finding the 70th percentile involves the same process. You calculate the z-score that corresponds to the cumulative area of 0.70 to find k such that 70 percent of the scores are below k.