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A highly mobile insect is placed into a glass tube with an inside diameter of 1 cm and a length of te The ends of the tube are labeled left and right. The insect moves randomly throughout tme tube. After the insect has been in the tube for a long time its distance from the left end in Meters is determined. This distance is denoted y d. Draw by hand what you expect a relative frequency histogram of the random variable y b. c. o look like. Give the location and value of the mean or median on the abscissa of your histogram. Draw by hand what you expect a cumulative relative frequency histogram of the random variable y to look like. Be sure to indicate the scale of the abscissa of your histogram. Draw by hand what you expect a relative frequency histogram of the square root transform of y to look like. Be sure to give the location and value of the median on the abscissa of your histogram. Draw by ha y to look like. Be sure to give the location and value of the median on the abscissa of your histogram. d. nd what you expect a relative frequency histogram of the square transform of
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Answer #1

Inside diameter of the glass: Length of the glass: mean distance travelled by insect : 1000 Standard deviation of mobil insects σ: 10 d-10.mm 10043771 1017.603 | 993.527l l:-1000.mm 1005.51 1015.465 1 50 randomly generated lengths 981.784 -rnorm (50 , μ , σ) |1013.079 989.511 Minimum value of X min (y)-980.834 N-length (y)-50 1004.591 | 989.478 | |987.579 | | 1004.241 | 1 Maximum value of X max (y)-1021.144 Range of X values: Range-max (y)-min(y) 40.31 Class Interval: Interval[min(y) max (y)]-[980.834 1021.144]Starting value just below minimum of X: c-min (u)-0.015-980.819 Number of desired classes widths: Width of each of the k intervals wーRange-4030951 | 3 | nth Interval of the class interval: Class intervals decomposed cc+n.uw Starting value of class limits. Lo-etd-980919 Class limits(minimum): LL+n-(u) Class limits(maximum): M-(L-0.1-n.(w) Class marks and frequency grouped: H-histogram! 0.015- 980.819 「01 2 4 k: 10 6 7 81 9 10 0 d:= 0.1Class marks CM submatrix (H,0,k-1,0,0) Frequency of X within the class limits: fsubmatrix (H,0,k-1,1,1) Relative frequency or density histogram: h- Class inteval Class limits Class mark Frequency c-980.819 c 984.85 L-980.919 M-984.85 CM-984.9 f-2 c -984.85 c -988.881 L984.95 M -988.881 CM-988.931 f -8 с 988.881 с 992.912 L-988.981 ΛΊ-992.912 CM-992.962 f_6 с 992.912 с 996.943 L-993.012 M-996.943 CM-996.993 f_4 C-996.943 c -1.001.10 L - 997.043 M -1.001.10CM -1.001.103f -5 0 0 0 3 3 3С6-1.005-103c7-1009-1031-1.001-10M5-1.005-10 NI I.005-10,-13 L-1.005.10M -1.009.10CM -1.009.1o3f -5 6 13 121 10 9- 8 7 6 2 984.5 988 991.5 995 998.5 1.002-103 1.006-103 1.009-103 1.013-103 1.016-103 1.02-103 1.023-103 CMusing the class marks weighted with their respective frequencies. k-1 n) i=0 k-1 n-1) i-0 k-1 . Σ f..(u,-u--=42.009472 1) i=0

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