Answer with Step-by-step explanation:
We are given that
For each real number
To prove that f is one -to-one.
Proof:Let and
be any nonzero real numbers such that
By using the definition of f to rewrite the left hand side of this equation
Then, by using the definition of f to rewrite the right hand side of this equation of
Equating the expression then we get
Therefore, f is one-to-one.
Answer:
a) The percentage of athletes whose GPA more than 1.665 is 87.49%.
b) John's GPA is 3.645.
Step-by-step explanation:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a)Find the percentage of athletes whose GPA more than 1.665.
This is 1 subtracted by the pvalue of Z when X = 1.665. So
has a pvalue of 0.1251
1 - 0.1251 = 0.8749
The percentage of athletes whose GPA more than 1.665 is 87.49%.
b) John's GPA is more than 85.31 percent of the athletes in the study. Compute his GPA.
His GPA is X when Z has a pvalue of 0.8531. So it is X when Z = 1.05.
John's GPA is 3.645.