In a particle size distribution experiemtn, a certain soil sample was examined and the size of all particles measured. In this unusual soil only 6 sizes of particles were found, and the percentages of soil particles in the differnent size groups were found to be:
Size(in microns) --- % of soil particles
100 --- 15
300 --- 12
500 --- 18
750 --- 35
1250 --- 15
1500 --- 5
Now, a single particle is selected at random, and its size (X) is measured.
a) Fine the probability density function of the particle size.
b) Give the cumulative distribution function in tabular and graphic form.
c) Find P[400 < X (less than or equal) 1300].
d) Find the mean and standard deviation of the distribution.
I don't expect anyone to answer b) fully, but as for the others, I'd be grateful for help on. Thanks.
2007-02-05 18:14:13 · 1 answers · asked by pertinential 5 in Science & Mathematics ➔ Other - Science
Show steps to numerical answers? ^^;;
2007-02-06 02:50:01 · update #1
a)
P(x) = 0.136507133 + 0.000485546x - 4.67333E-06x^2 + 1.28271E-08x^3 - 1.19063E-11x^4 + 3.514E-15x^5
b)
100 -- .15
300 -- .27
500 -- .45
750 -- .80
1250 -- .95
1500 -- 1.00
100 -- ***.15
300 -- *****.27
500 -- ***** ***.45
750 -- ***** ***** ****.80
1250 -- ***** ***** ***** *.95
1500 -- ***** ***** ***** **1.00
c) 0.95
100 --- -65 15 -975 -6.416 617.47584
300 --- -45 12 -540 -4.416 234.012672
500 --- -25 18 -450 -2.416 105.067008
750 ---... 0 35. . . 0 0.084..... 0.24696
1250 --- 50 15.. 750 5.084. 387.70584
1500 --- 75.. 5.. 375 7.548. 287.58528
. . . . . . . . 100 -840. . . . . 1632.0936
m = -8.4 + 750 = 741.6
σ = 404
2007-02-05 20:06:53 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋