Brian bought a fish tank that is 22 in. long, 12 in. wide, and 16 in. tall. Which is the volume of the fish tank?
2 answers:
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Sum :
Term : 1, and
Product : and
Factor : 5 and x, 3 and y, 9 and 5x+1
Quotient :
Coefficient : 5 is the coefficient of x and 3 is the coefficient of y.
Explanation:
The expression is
Sum: Sum is the result of addition of terms.
Thus, from the expression,
Sum =
Term : A term is a single number or a variable or a number multiplied with a variable.
Thus, from the expression,
Term = 1, and
Product : Product is the result of multiplication of numbers.
Thus, from the expression,
Product = and
Factor : The numbers that are multiplied is called a factor.
Thus, from the expression,
Factor = 5 and x, 3 and y, 9 and 5x+1
Quotient : Quotient is the result of dividing two numbers or variables.
Thus, the given whole expression is a quotient.
Hence, Quotient =
Coefficient : Coefficient of a variable is a number multiplied with a variable.
Thus, from the expression,
Coefficient : 5 is the coefficient of x and 3 is the coefficient of y.
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.
