Answer to Question #189713 in Statistics and Probability for prince

Question #189713

Consider the following data: 


86 144 81 72 97 110 87 106 118 92

103 132 108 107 80 91 84 98 120 70

110 96 82 99 110 117 83 85 92 83

86 125 87 104 57 46 92 86 92 110

110 66 148 80 109 95 107 99 94 108

89 118 83 102 70 88 163 89 131 98

104 130 88 75 91 97 76 94 151 89

108 97 87 107 117 100 74 108 106 103

104 80 134 92 115 91 123 97 84 106

96 65 100 87 86 110 102 96 94 161


(a) Form a frequency table and plot a frequency distribution of this data.

(b) Calculate the mean value of the data.

(c) Find the equation for the normal distribution that would fit the data as closely as possible.

(d) Plot the normal distribution curve that is described by this equation. 


1
Expert's answer
2021-05-14T05:11:02-0400

(a)




Frequency Distribution:






(b) Mean = "\\dfrac{Sum\\ of\\ all\\ numbers}{data}=\\dfrac{\\sum x_i}{n}"


"\\Rightarrow \\mu =\\dfrac{9900}{100}=99"


Variance "\\sigma^2= \\dfrac{\\sum (x-\\mu)^2}{n}"

"\\Rightarrow \\sigma^2=\\frac{40740}{100}=407.4"


Standard Deviation "\\sigma=\\sqrt{\\dfrac{40740}{100}}=\\sqrt{407.4}=20.1841"


(c) Probability distribution function for normal distribution

"pdf=\\dfrac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\dfrac{1}{2}(\\dfrac{x-\\mu}{\\sigma})^2}"


So, Required equation "=\\dfrac{1}{20.1842\\sqrt{2\\pi}}e^{-\\frac{1}{2}(\\frac{x-99}{20.1842})^2}"


(d)

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Comments

Assignment Expert
03.06.21, 11:29

Dear Prince,

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Prince
14.05.21, 12:19

Thanks a lot

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