Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
<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.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters are given as follows:
Item a:
The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:
Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:
By the Central Limit Theorem:
Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
(c) 5y -17x +99 = 0
Step-by-step explanation:
The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.
<h3>Midpoint</h3>
The midpoint of XZ is the average of the coordinates of X and Z.
M = (X +Z)/2
M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)
<h3>Line through two points</h3>
The slope of the median can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
The slope of line YM is ...
m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The line with slope 17/5 through point Y(7, 4) is ...
y -4 = 17/5(x -7)
Subtracting the right side, and multiplying by 5 gives ...
5(y -4) -17(x -7) = 0
5y -17x +99 = 0 . . . . equation of the median through Y
Answer:
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Step-by-step explanation:
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Answer:
P = 20x + 6
Step-by-step explanation:
Perimeter formula:
P = 2(l + w)
Given:
l = 8x - 1
w = 2x + 4
Work:
P = 2(l + w)
P = 2(8x - 1 + 2x + 4)
P = 2(10x + 3)
P = 20x + 6
