Answer:
Step-by-step explanation:
For the null hypothesis,
H0: p = 88
For the alternative hypothesis,
Ha: p < 88
Considering the population proportion, probability of success, p = 0.88
q = probability of failure = 1 - p
q = 1 - 0.88 = 0.12
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 21
n = number of samples = 32
P = 21/32 = 0.66
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.66 - 0.88)/√(0.88 × 0.12)/32 = - 3.83
The corresponding p value would be determined by looking at the normal distribution table for the area below the z score. Therefore,
P value = 0.00006
Answer:
![x-4y+4=0](https://tex.z-dn.net/?f=x-4y%2B4%3D0)
and x=4
Step-by-step explanation:
We are given that a curve
![y=\sqrt x](https://tex.z-dn.net/?f=y%3D%5Csqrt%20x)
We have to find the equation of tangent at point (4,2) on the given curve.
Let y=f(x)
Differentiate w.r.t x
![f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%20x%7D)
By using the formula ![\frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28%5Csqrt%20x%29%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%20x%7D)
Substitute x=4
Slope of tangent
![m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}](https://tex.z-dn.net/?f=m%3Df%27%28x%29%3D%5Cfrac%7B1%7D%7B2%5Csqrt%204%7D%3D%5Cfrac%7B1%7D%7B2%5Ctimes%202%7D%3D%5Cfrac%7B1%7D%7B4%7D)
In given question
![m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}](https://tex.z-dn.net/?f=m%3D%5Clim_%7Bx%5Crightarrow%20a%7D%5Cfrac%7Bf%28x%29-f%28a%29%7D%7Bx-a%7D)
![\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%3D%5Clim_%7Bx%5Crightarrow%204%7D%5Cfrac%7Bf%28x%29-f%284%29%7D%7Bx-4%7D)
By comparing we get a=4
Point-slope form
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Using the formula
The equation of tangent at point (4,2)
![y-2=\frac{1}{4}(x-4)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B1%7D%7B4%7D%28x-4%29)
![4y-8=x-4](https://tex.z-dn.net/?f=4y-8%3Dx-4)
![x-4y-4+8=0](https://tex.z-dn.net/?f=x-4y-4%2B8%3D0)
![x-4y+4=0](https://tex.z-dn.net/?f=x-4y%2B4%3D0)
Mean number of errors in each page = 0.01
Mean number of errors in 100 pages = 0.01*100=1
It is possible to use the cumulative distribution function (CMF), but the math is a little more complex, involving the gamma-function. Tables and software are available for that purpose.
Thus it is easier to evaluate with a calculator for the individual cases of k=0,1,2 and 3.
The Poisson distribution has a PMF (probability mass function)
![](https://tex.z-dn.net/?f=)
![P(k):=\frac{\lambda^ke^{-\lambda}}{k!}](https://tex.z-dn.net/?f=P%28k%29%3A%3D%5Cfrac%7B%5Clambda%5Eke%5E%7B-%5Clambda%7D%7D%7Bk%21%7D)
with λ = 1
=>
![P(0):=\frac{1^0e^{-1}}{0!}=0.3678794](https://tex.z-dn.net/?f=P%280%29%3A%3D%5Cfrac%7B1%5E0e%5E%7B-1%7D%7D%7B0%21%7D%3D0.3678794)
![P(1):=\frac{1^1e^{-1}}{1!}=0.3678794](https://tex.z-dn.net/?f=P%281%29%3A%3D%5Cfrac%7B1%5E1e%5E%7B-1%7D%7D%7B1%21%7D%3D0.3678794)
![P(2):=\frac{1^2e^{-1}}{2!}=0.1839397](https://tex.z-dn.net/?f=P%282%29%3A%3D%5Cfrac%7B1%5E2e%5E%7B-1%7D%7D%7B2%21%7D%3D0.1839397)
![P(3):=\frac{1^3e^{-1}}{3!}=0.0613132](https://tex.z-dn.net/?f=P%283%29%3A%3D%5Cfrac%7B1%5E3e%5E%7B-1%7D%7D%7B3%21%7D%3D0.0613132)
=>
![P(k](https://tex.z-dn.net/?f=P%28k%3C%3D3%29%3DP%280%29%2BP%281%29%2BP%282%29%2BP%283%29%3D0.9810118)
or
P(k<=3)=
0.9810 (to four decimal places)
Answer:
x = 2/5
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
<u>Step 1: Write equation</u>
5x = 2
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide both sides by 5: x = 2/5
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution</em>.
- Substitute: 5(2/5) = 2
- Multiply: 10/5 = 2
- Divide: 2 = 2
Answer:
(-1,9)
(0,3)
(1,-3)
(5,-27)
Step-by-step explanation:
Plug x values into the equation.