Answer:
B) approximately normal with mean 2.3 and standard deviation 2
Step-by-step explanation:
Given the following :
Mean crimes per day = 2.3
Standard deviation = 2
Number of samples = 100
Sampling distribution of the mean:
According to the central limit theorem:
Sample mean = population mean
2.3 = 2.3
The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.
s = population standard deviation / √sample size
s = 2 / √100
s = 2 / 10
s = 0.2
The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.
Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2
<h2>Answer-Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:</h2><h2 /><h2>A(x) = \frac{f(b)-f(a)}{b-a}A(x)= </h2><h2>b−a</h2><h2>f(b)−f(a)</h2><h2> </h2><h2> </h2><h2 /><h2>Given the function:</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^xf(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>x</h2><h2> </h2><h2 /><h2>We have to find the average rate of change from x = 1 to x= 2</h2><h2 /><h2>At x = 1</h2><h2 /><h2>then;</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^1 = 5f(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>1</h2><h2> =5</h2><h2 /><h2>At x = 2</h2><h2 /><h2>then;</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^2=20 \cdot \frac{1}{16} = 1.25f(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>2</h2><h2> =20⋅ </h2><h2>16</h2><h2>1</h2><h2> </h2><h2> =1.25</h2><h2 /><h2>Substitute these in above formula we have;</h2><h2 /><h2>A(x) = \frac{f(2)-f(1)}{2-1}A(x)= </h2><h2>2−1</h2><h2>f(2)−f(1)</h2><h2> </h2><h2> </h2><h2 /><h2>⇒A(x) = \frac{1.25-5}{1}=-3.75A(x)= </h2><h2>1</h2><h2>1.25−5</h2><h2> </h2><h2> =−3.75</h2><h2 /><h2>therefore, average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75</h2>
<h2>Please Mark me as brainlist. </h2>
An equation is formed of two equal expressions. The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given graph is the graph of an exponential function, the general equation of an exponential function is given by the y=aeᵇˣ. To get the function f(x) and g(x), you need to substitute the points in the given function and produce the equation of each function.
The equation for f(x) from the given graph can be written as,
Now, similarly from the graph the function of g(x) can be written as,
Further, the equation of function g(x) in terms of f(x) can be written as,
g(x) = -3[f(x)]
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