A football stadium holds 52,000 fans. A college student is doing research and determines that on any given game day, the home te
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Answer:
b. [278.90, 288.55]
See the explanation below.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the amounts of energy of a population, and for this case we know the distribution for X is given by:
Where and
LOWER LIMIT
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 25% of data from the top 75% is 278.90.
UPPER LIMIT
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.7 of the area on the left and 0.3 of the area on the right it's z=0.524. On this case P(Z<0.524)=0.7 and P(z>0.524)=0.3
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 70% of data from the top 30% is 289.78.
With the procedure we got for the limits [278.9 , 289.78]
And since any of the options are on the list we take th most similar for this case:
b. [278.90, 288.55]
Answer:
x-2 is a factor of following polynomials:
- b(x) = 3x² + 15x - 42
- d(x) = 3x³ - 2x² - 15x + 14
- e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70
Step-by-step explanation:
In order to check that which polynomials might have x-2 as a factor, we will put
x-2 = 0 => x = 2 in each polynomial, if the value of polynomial on 2 is zero then x-2 is a factor otherwise not.
So,
a(x) = 6x² - 7x - 5
Putting x = 2
b(x) = 3x² + 15x - 42
c(x) = 2x³ + 13x² + 16x + 5
d(x) = 3x³ - 2x² - 15x + 14
e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70
Hence,
x-2 is a factor of following polynomials:
- b(x) = 3x² + 15x - 42
- d(x) = 3x³ - 2x² - 15x + 14
- e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70