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The variable is
X: blood platelet count of a woman
This variable has a bell shaped distribution (Normal)
With mean μ=261.1 and standard deviation σ=64.3
a.
The platelet count within 3 standard deviations of the mean can be calculated as
μ±3σ
You can symbolize it as
μ-3σ ≤ X ≤ μ+3σ
According to the empirical rule of the normal distribution you know that under any bell shaped distribution:
Between μ ± σ you'll find the 68% of the distribution
Between μ ± 2σ you'll find the 95% of the distribution
Between μ ± 3σ you'll find the 99% of the distribution
So following this rule you'll find 99% of the women with platelet count within 3 standard deviations of the mean.
b.
3% of the population is found between a vertain interval, the rest 97% is separated in equal tails around this interval.
Divide 0.97 by 2
0.97/2= 0.485
Each tail contains 0.485 of the distribtuion.
a and b represent the values within you'll find 3% of the population.
Until a you'll find 0.485 of the population and until b you'll find 0.485+0.03=0.515
To calculate both unknown values you have to use the standard normal distribution. This distribution is centered in zero, the left tail is negative and the right tail is positive.
a and b are at a equal distance from the mean but with different sign, so you only have to calculate on and then you invert the sign to get the other one.
I'll calculate the positive value:
Z= (X- μ )/σ~N(0,1)
P(Z≤ b)=0.515
Look in the body of the Z-table, rigth or positive entry and reach the margins for the value:
b= 0.038
Then using the values of the mean and the standard deviation you can calculate the corresponding valueof platelet count:
b= (X- μ )/σ
0.038= (X- 261.1 )/64.3
0.038*64.3=X-261.1
2.4434+261.1=X
X=263.5434=263.5
a=-b=-0.038
a= (X- μ )/σ
-0.038= (X- 261.1 )/64.3
-0.038*64.3=X-261.1
-2.4434+261.1=X
X=258.6566= 258.7
3% of the populations platelet count is between 258.7 and 263.5.
Answer:
(0, -4)
Step-by-step explanation:
The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)
The ratio the required point partitions the line = 2 to 3
The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;
Therefore, the required point is located as follows;
The coordinates of the point is (0, -4)
Let
<span>A------> (−3, −11)
B------> (6, 4)
step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3
step 2
with m=5/3 and point B (6, 4) find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6
case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3
case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0
y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)
y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)
case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because
if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0
y=35x−6-------> y=-6
the y intercept is the point (0,-6)
y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)
they have the same y-intercept but the two lines are not perpendicular
see the attached figure
<span>A------> (−3, −11)
B------> (6, 4)
step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3
step 2
with m=5/3 and point B (6, 4) find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6
case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3
case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0
y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)
y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)
case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because
if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0
y=35x−6-------> y=-6
the y intercept is the point (0,-6)
y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)
they have the same y-intercept but the two lines are not perpendicular
see the attached figure