A) Word-processing program is an example of a software
B= -2x+5-2x^2-ax
A= -2x+5-2x^2-b/x
x=0
Answer:
(a)
and ![\sum x_i^2=197.46](https://tex.z-dn.net/?f=%5Csum%20x_i%5E2%3D197.46)
(b) The sample variance is
and the sample standard deviation is ![s=0.728](https://tex.z-dn.net/?f=s%3D0.728)
Step-by-step explanation:
(a)
The sum of these 17 sample observations is
![\sum x_i=2.79\:+2.57+\:2.73\:+3.75\:+2.27+\:2.75+\:4.00+\:4.22+\:3.88+\:4.35+\:3.41+\:4.57+\:2.38+\:3.73\:+2.75+\:3.47+\:3.06\\\\\sum x_i=56.68](https://tex.z-dn.net/?f=%5Csum%20x_i%3D2.79%5C%3A%2B2.57%2B%5C%3A2.73%5C%3A%2B3.75%5C%3A%2B2.27%2B%5C%3A2.75%2B%5C%3A4.00%2B%5C%3A4.22%2B%5C%3A3.88%2B%5C%3A4.35%2B%5C%3A3.41%2B%5C%3A4.57%2B%5C%3A2.38%2B%5C%3A3.73%5C%3A%2B2.75%2B%5C%3A3.47%2B%5C%3A3.06%5C%5C%5C%5C%5Csum%20x_i%3D56.68)
and the sum of their squares is
![\sum x_i^2=2.79^2\:+2.57^2+\:2.73^2\:+3.75^2\:+2.27^2+\:2.75^2+\:4.00^2+\:4.22^2+\:3.88^2+\:4.35^2+\:3.41^2+\:4.57^2+\:2.38^2+\:3.73^2\:+2.75^2+\:3.47^2+\:3.06^2\\\\\sum x_i^2=197.46](https://tex.z-dn.net/?f=%5Csum%20x_i%5E2%3D2.79%5E2%5C%3A%2B2.57%5E2%2B%5C%3A2.73%5E2%5C%3A%2B3.75%5E2%5C%3A%2B2.27%5E2%2B%5C%3A2.75%5E2%2B%5C%3A4.00%5E2%2B%5C%3A4.22%5E2%2B%5C%3A3.88%5E2%2B%5C%3A4.35%5E2%2B%5C%3A3.41%5E2%2B%5C%3A4.57%5E2%2B%5C%3A2.38%5E2%2B%5C%3A3.73%5E2%5C%3A%2B2.75%5E2%2B%5C%3A3.47%5E2%2B%5C%3A3.06%5E2%5C%5C%5C%5C%5Csum%20x_i%5E2%3D197.46)
(b)
The sample variance, denoted by
, is given by
![s^2=\frac{S_{xx}}{n-1}](https://tex.z-dn.net/?f=s%5E2%3D%5Cfrac%7BS_%7Bxx%7D%7D%7Bn-1%7D)
where ![S_{xx} =\sum x_i^2-\frac{(\sum x_i)^2}{n}](https://tex.z-dn.net/?f=S_%7Bxx%7D%20%3D%5Csum%20x_i%5E2-%5Cfrac%7B%28%5Csum%20x_i%29%5E2%7D%7Bn%7D)
Applying the above formula we get that
![S_{xx}=197.46-\frac{(56.68)^2}{17}\\\\S_{xx} =8.482](https://tex.z-dn.net/?f=S_%7Bxx%7D%3D197.46-%5Cfrac%7B%2856.68%29%5E2%7D%7B17%7D%5C%5C%5C%5CS_%7Bxx%7D%20%3D8.482)
![s^2=\frac{8.482}{17-1}=0.530](https://tex.z-dn.net/?f=s%5E2%3D%5Cfrac%7B8.482%7D%7B17-1%7D%3D0.530)
The sample standard deviation, denoted by <em>s</em>, is the (positive) square root of the variance:
![s=\sqrt{s^2}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7Bs%5E2%7D)
Applying the above formula we get that
![s=\sqrt{0.530}=0.728](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B0.530%7D%3D0.728)
93 students play an instrument because you would take 310 (the total amount of students) and multiply it by 0.3 (the thirty percent) and get 93