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The bell curve attached below shows the normal distribution of the data.
We are looking the value of X such as the area to its left gives the probability of 0.75
We first need the z-score which we can obtain by reading from the z-table (as shown in the second picture below)
The z-score is = 0.7734
Then we use the following formula to work out X
z-score = (X - Mean) ÷ Standard Deviation
0.7734 = (X - 100) ÷ 15
0.7734×15 = X - 100
11.601 = X - 100
X = 11.601 + 100
X = 111.601 ≈ 112
Hence the third quartile is 112
We are looking the value of X such as the area to its left gives the probability of 0.75
We first need the z-score which we can obtain by reading from the z-table (as shown in the second picture below)
The z-score is = 0.7734
Then we use the following formula to work out X
z-score = (X - Mean) ÷ Standard Deviation
0.7734 = (X - 100) ÷ 15
0.7734×15 = X - 100
11.601 = X - 100
X = 11.601 + 100
X = 111.601 ≈ 112
Hence the third quartile is 112
The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x ² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x ² -7x + 10 = 0
Factorizing the middle term, we get:
x ² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.
