Answer:
The minimum height in the top 15% of heights is 76.2 inches.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
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:

Find the minimum height in the top 15% of heights.
This is the value of X when Z has a pvalue of 0.85. So it is X when Z = 1.04.




The minimum height in the top 15% of heights is 76.2 inches.
14.75x - 23=5.25x+45.2
14.75x-23-5.25x=5.25x+45.2-5.25x
14.75-5.25x=9.5
9.5x-23=45.2
9.5x-23+23=45.2+23
9.5x=68.2
9.5x/9.5=68.2/9.5
x=7.178947
The options of the problem are

we have

we know that
<u>The Rational Root Theorem </u>states that when a root 'x' is written as a fraction in lowest terms
p is an integer factor of <u>the constant term</u>, and q is an integer factor of <u>the coefficient of the first monomial</u>.
So
in this problem
the constant term is equal to 
and the first monomial is equal to
-----> coefficient is 
therefore
<u>the answer is the option </u>
D. 