1. At the gym on Monday, Larry is told to up his weight on the bench-press by 15% from last week. Last week he was bench-pressin
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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:
The number is 12.
Step-by-step explanation:
Given:
We need to find a number multiply to each term to get rid of fraction.
We will find LCD of denominator.
First we see the numbers at denominator
Denominators are 4,3,2
Now, we will find the LCD of 2,3, and 4
Factor of 2: 2x1
Factor of 3: 3x1
Factor of 4: 2x2x1
LCD = 2x2x3 = 12
If we multiply by 12 to each term to eliminate the fraction.
Simplest equation:
Hence, The number is 12.