Given:
The table of values for the function f(x).
To find:
The values and
.
Solution:
From the given table, it is clear that the function f(x) is defined as:
We know that if (a,b) is in the function f(x), then (b,a) must be in the function . So, the inverse function is defined as:
And,
...(i)
Using (i), we get
Now,
Therefore, the required values are and
.
Answer: Prokhorova is more outstanding.
Step-by-step explanation: To compare scores from different distributions, first standardize it:
z-score =
where
x is the individual mean you want to compare
μ is the mean of the population
σ is standard deviation
For <u>Gertrud Bacher</u>:
z-score =
z-score = (s)
The negative sign indicates Bacher's mean is less than the mean
For <u>Yelena Prokhorova</u>:
z-score =
z-score = 2 (cm)
The positive sign indicates Prokhorova's mean is more than the mean.
Using z-score table, you determine the percentiles are:
For Bacher: Percentile = 5.5%
For Prokhorova: Percentile = 97.7%
Bacher's percentile means she is above 5.5% of the participants, while Prokhorova is 97.7% above the other competitors, which means Prokhorova have a better performance and deserves more points.