The force acting on a beam was measured under the same operating conditions and a sample of 5 data points was collected. This process was repeated by 3 observers. The pooled standard deviations of these 3 data sets was 1.21. Determine the true mean force using all pooled data (with a 95% probability). The result should look like this: True mean = mean +/- Margin of Error

± 1.51

Explanation:

The mean standard deviation = 1.21 since the three data sets had 1.21 standard deviations each

95% probability = 0.95

calculate standard error is calculated as = =

=  

=    =  =  0.6928

calculate the margin of error

from statistical table equation  becomes

2.179 * 0.6928 = 1.5096 ≈   ± 1.51

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.