Let x be a random variable representing the heights of adult American men. Since it is normally distributed and the population mean and standard deviation are known, we would apply the formula,
z = (x - mean)/Standard deviation
From the information given,
mean = 68
standard deviation = 2.5
The probability that the height of a selected adult is between 63 and 73 is expressed as
For x = 63,
z = (63 - 68)/2.5 = -2
Looking at the normal distribution table, the probability corresponding to the z score is 0.02275
For x = 73,
z = (73 - 68)/2.5 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.97725
Therefore,
Thus, the percentage of men are between 63 and 73 is
0.9545 * 100 = 95.45%
Rounding up to the nearest percentage, the answer is 95%
a) because it is equal to the area of the shaded region between X=4 and X=6, and the probability that X falls within some interval is given by the area under the PDF.
b) because the shaded region is a rectangle of height 1/5 (by virtue of X following a uniform distribution over the interval [2, 7], which has length 5).
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
Answer:
Therefore 200.96 ft.of fencing are needed to go around the pool path.
Step-by-step explanation:
Given, a circular swimming pool has a radius of 28ft. There is a path all the way around the pool. The width of the path 4 ft.
The radius of the outside edge the pool path is
= Radius of the pool + The width of the path
= (28+4) ft
= 32 ft.
To find the length of fencing, we need to find the circumference of outside the pool path.
Here r= 32 ft
The circumference of outside edge of the pool path
=
=200.96 ft.
Therefore 200.96 ft.of fencing are needed to go around the pool path.