Z- score is a statistical tool that is used to determine the probability of finding a number or a value under a normal distribution plot. A normal distribution assumes that the mean is equal to zero and that the standard deviation is equal to 1. Using the z-score table, we can find the probability either on the right side or the left side. Using the table hence, we find the probability to the left of the value. The probability that is equivalent to the unknown z should be equal to 0.5 + (0.27/2) = 0.635. 0.5 comes from the assumption that the area under the curve on each side is 50% of the total. The equivalent z score is equal to z = 0.345.
So hmmm check the picture below
in an isosceles triangle, two sides are equal, and thus the angles those twin legs make, are also twin angles
let's say the angle made is "a", so all internal angles will be 64 + a + a = 180
or 64 + 2a = 180
thus 2a = 180 - 64 => 2a = 116, thus a = 116/2
A parent function is normally not streched or anything or shhifted
y=kx or
y=x^a or
y=a^x are exapmles
y=x is y=1x
y=2x^3 is not it because the parent would be y=x^3
y=1/x is y=x^-1
y=2^x is y=2^x
answer is 2x^3 is not a parent function
Using the normal distribution, it is found that the replacement time that separates the top 18% from the bottom 82% is of 11.23 years.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are, respectively, given by
.
The desired value is the 82nd percentile, which is X when Z = 0.915, hence:


X - 9.4 = 0.915(2)
X = 11.23
The replacement time that separates the top 18% from the bottom 82% is of 11.23 years.
More can be learned about the normal distribution at brainly.com/question/24663213
In mathematics, two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant multiplier. The constant is called the coefficient of proportionality or proportionality constant.