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FGCU / Math / MATH 2023 / What are the properties of a normal distribution?

What are the properties of a normal distribution?

What are the properties of a normal distribution?

Description

School: Florida Gulf Coast University
Department: Math
Course: Statistical Methods
Professor: Rona axelrod
Term: Fall 2016
Tags: Statistics and distribution
Cost: 25
Name: Chapter 7 Notes, Fundamentals of Statistics
Description: 7.1- Properties of a Normal Distribution 7.2- Applications of a Normal Distribution 7.3- Assessing Normality
Uploaded: 10/30/2016
4 Pages 134 Views 0 Unlocks
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"}.lst-kix_ll3ulrdzmx5d-1 > li:before{content:"(" counter(lst-ctn-kix_ll3ulrdzmx5d-1,lower-roman) ") "}.lst-kix_ll3ulrdzmx5d-6 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-6}.lst-kix_ll3ulrdzmx5d-2 > li:before{content:"(" counter(lst-ctn-kix_ll3ulrdzmx5d-2,decimal) ") "}ol.lst-kix_5n2ou0hlvomq-3.start{counter-reset:lst-ctn-kix_5n2ou0hlvomq-3 0}ol.lst-kix_xqyjtmw56zpv-0.start{counter-reset:lst-ctn-kix_xqyjtmw56zpv-0 0}.lst-kix_97b6r4n2nnjf-1 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-1}.lst-kix_ll3ulrdzmx5d-7 > li:before{content:"" counter(lst-ctn-kix_ll3ulrdzmx5d-7,lower-roman) ". "}.lst-kix_ll3ulrdzmx5d-6 > li:before{content:"" counter(lst-ctn-kix_ll3ulrdzmx5d-6,lower-latin) ". 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"}ul.lst-kix_9yokpth8l7z2-1{list-style-type:none}ul.lst-kix_9yokpth8l7z2-0{list-style-type:none}ul.lst-kix_9yokpth8l7z2-5{list-style-type:none}ul.lst-kix_9yokpth8l7z2-4{list-style-type:none}ul.lst-kix_9yokpth8l7z2-3{list-style-type:none}ol.lst-kix_dbkwut90ew6e-4.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-4 0}ul.lst-kix_9yokpth8l7z2-2{list-style-type:none}ul.lst-kix_9yokpth8l7z2-8{list-style-type:none}.lst-kix_iixp2sb6ta62-7 > li:before{content:"- "}.lst-kix_iixp2sb6ta62-8 > li:before{content:"- "}ul.lst-kix_9yokpth8l7z2-7{list-style-type:none}ul.lst-kix_9yokpth8l7z2-6{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-4.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-4 0}.lst-kix_iixp2sb6ta62-6 > li:before{content:"- "}.lst-kix_5n2ou0hlvomq-5 > li{counter-increment:lst-ctn-kix_5n2ou0hlvomq-5}ul.lst-kix_temc2asnmng8-8{list-style-type:none}ul.lst-kix_b5zvstllercd-0{list-style-type:none}ul.lst-kix_temc2asnmng8-6{list-style-type:none}ul.lst-kix_b5zvstllercd-2{list-style-type:none}ul.lst-kix_temc2asnmng8-7{list-style-type:none}ul.lst-kix_b5zvstllercd-1{list-style-type:none}ul.lst-kix_temc2asnmng8-4{list-style-type:none}ul.lst-kix_temc2asnmng8-5{list-style-type:none}ul.lst-kix_temc2asnmng8-2{list-style-type:none}ul.lst-kix_temc2asnmng8-3{list-style-type:none}ul.lst-kix_temc2asnmng8-0{list-style-type:none}ul.lst-kix_temc2asnmng8-1{list-style-type:none}ul.lst-kix_6za6fk6n623r-0{list-style-type:none}ul.lst-kix_6za6fk6n623r-1{list-style-type:none}ul.lst-kix_6za6fk6n623r-2{list-style-type:none}ul.lst-kix_6za6fk6n623r-3{list-style-type:none}ul.lst-kix_6za6fk6n623r-4{list-style-type:none}.lst-kix_dbkwut90ew6e-5 > li{counter-increment:lst-ctn-kix_dbkwut90ew6e-5}ul.lst-kix_6za6fk6n623r-5{list-style-type:none}ul.lst-kix_6za6fk6n623r-6{list-style-type:none}ul.lst-kix_6za6fk6n623r-7{list-style-type:none}ul.lst-kix_6za6fk6n623r-8{list-style-type:none}ul.lst-kix_b5zvstllercd-4{list-style-type:none}ol.lst-kix_dbkwut90ew6e-5.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-5 0}ul.lst-kix_b5zvstllercd-3{list-style-type:none}ol.lst-kix_xqyjtmw56zpv-1.start{counter-reset:lst-ctn-kix_xqyjtmw56zpv-1 0}ul.lst-kix_b5zvstllercd-6{list-style-type:none}ul.lst-kix_b5zvstllercd-5{list-style-type:none}ul.lst-kix_b5zvstllercd-8{list-style-type:none}ul.lst-kix_b5zvstllercd-7{list-style-type:none}.lst-kix_6za6fk6n623r-0 > li:before{content:"● "}.lst-kix_97b6r4n2nnjf-5 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-5}.lst-kix_3uayykrrfdcf-2 > li:before{content:"- "}.lst-kix_6za6fk6n623r-1 > li:before{content:"○ "}.lst-kix_xqyjtmw56zpv-1 > li{counter-increment:lst-ctn-kix_xqyjtmw56zpv-1}.lst-kix_3uayykrrfdcf-1 > li:before{content:"- "}.lst-kix_3uayykrrfdcf-0 > li:before{content:"- "}.lst-kix_6za6fk6n623r-2 > li:before{content:"■ "}.lst-kix_ll3ulrdzmx5d-8 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-8}.lst-kix_6za6fk6n623r-5 > li:before{content:"■ "}.lst-kix_ll3ulrdzmx5d-2 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-2}ol.lst-kix_5n2ou0hlvomq-4.start{counter-reset:lst-ctn-kix_5n2ou0hlvomq-4 0}.lst-kix_6za6fk6n623r-3 > li:before{content:"● "}.lst-kix_6za6fk6n623r-4 > li:before{content:"○ "}ol.lst-kix_dbkwut90ew6e-0{list-style-type:none}ol.lst-kix_dbkwut90ew6e-1{list-style-type:none}.lst-kix_97b6r4n2nnjf-7 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-7}ol.lst-kix_dbkwut90ew6e-4{list-style-type:none}ol.lst-kix_dbkwut90ew6e-5{list-style-type:none}ol.lst-kix_dbkwut90ew6e-2{list-style-type:none}ol.lst-kix_dbkwut90ew6e-3{list-style-type:none}.lst-kix_b5zvstllercd-1 > li:before{content:"- "}.lst-kix_b5zvstllercd-5 > li:before{content:"- "}ol.lst-kix_xqyjtmw56zpv-7.start{counter-reset:lst-ctn-kix_xqyjtmw56zpv-7 0}.lst-kix_6za6fk6n623r-7 > li:before{content:"○ "}.lst-kix_ll3ulrdzmx5d-1 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-1}.lst-kix_b5zvstllercd-7 > li:before{content:"- "}.lst-kix_dbkwut90ew6e-5 > li:before{content:"" counter(lst-ctn-kix_dbkwut90ew6e-5,decimal) ") "}ul.lst-kix_x4vq44w6jjzx-4{list-style-type:none}ul.lst-kix_x4vq44w6jjzx-3{list-style-type:none}.lst-kix_97b6r4n2nnjf-8 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-8}.lst-kix_3uayykrrfdcf-3 > li:before{content:"- "}ul.lst-kix_x4vq44w6jjzx-2{list-style-type:none}ul.lst-kix_x4vq44w6jjzx-1{list-style-type:none}.lst-kix_dbkwut90ew6e-3 > li:before{content:"" counter(lst-ctn-kix_dbkwut90ew6e-3,lower-latin) ") "}.lst-kix_dbkwut90ew6e-7 > li:before{content:"" counter(lst-ctn-kix_dbkwut90ew6e-7,lower-roman) ". "}ul.lst-kix_x4vq44w6jjzx-0{list-style-type:none}.lst-kix_pjtr9kuz4bg1-7 > li:before{content:"- "}.lst-kix_3uayykrrfdcf-5 > li:before{content:"- "}.lst-kix_3uayykrrfdcf-7 > li:before{content:"- "}.lst-kix_ll3ulrdzmx5d-0 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-0}ul.lst-kix_x4vq44w6jjzx-8{list-style-type:none}ul.lst-kix_x4vq44w6jjzx-7{list-style-type:none}ul.lst-kix_x4vq44w6jjzx-6{list-style-type:none}.lst-kix_pjtr9kuz4bg1-5 > li:before{content:"- "}ul.lst-kix_x4vq44w6jjzx-5{list-style-type:none}.lst-kix_b5zvstllercd-3 > li:before{content:"- "}ul.lst-kix_3uayykrrfdcf-8{list-style-type:none}ul.lst-kix_3uayykrrfdcf-4{list-style-type:none}ul.lst-kix_3uayykrrfdcf-5{list-style-type:none}ul.lst-kix_3uayykrrfdcf-6{list-style-type:none}.lst-kix_pjtr9kuz4bg1-3 > li:before{content:"- "}ul.lst-kix_3uayykrrfdcf-7{list-style-type:none}.lst-kix_dbkwut90ew6e-1 > li:before{content:"(" counter(lst-ctn-kix_dbkwut90ew6e-1,lower-roman) ") "}.lst-kix_xqyjtmw56zpv-8 > li{counter-increment:lst-ctn-kix_xqyjtmw56zpv-8}ol.lst-kix_ll3ulrdzmx5d-2.start{counter-reset:lst-ctn-kix_ll3ulrdzmx5d-2 0}ol.lst-kix_ll3ulrdzmx5d-5.start{counter-reset:lst-ctn-kix_ll3ulrdzmx5d-5 0}.lst-kix_pjtr9kuz4bg1-1 > li:before{content:"- "}ul.lst-kix_wid4yv736pj8-0{list-style-type:none}ul.lst-kix_wid4yv736pj8-1{list-style-type:none}ul.lst-kix_wid4yv736pj8-2{list-style-type:none}ol.lst-kix_dbkwut90ew6e-0.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-0 0}ul.lst-kix_wid4yv736pj8-3{list-style-type:none}ul.lst-kix_wid4yv736pj8-4{list-style-type:none}.lst-kix_iixp2sb6ta62-1 > li:before{content:"- "}.lst-kix_iixp2sb6ta62-5 > li:before{content:"- "}ul.lst-kix_wid4yv736pj8-5{list-style-type:none}ol.lst-kix_dbkwut90ew6e-8{list-style-type:none}ul.lst-kix_3uayykrrfdcf-0{list-style-type:none}ul.lst-kix_wid4yv736pj8-6{list-style-type:none}ul.lst-kix_3uayykrrfdcf-1{list-style-type:none}ul.lst-kix_wid4yv736pj8-7{list-style-type:none}.lst-kix_97b6r4n2nnjf-6 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-6}ol.lst-kix_dbkwut90ew6e-6{list-style-type:none}ul.lst-kix_3uayykrrfdcf-2{list-style-type:none}ul.lst-kix_wid4yv736pj8-8{list-style-type:none}ol.lst-kix_dbkwut90ew6e-7{list-style-type:none}ul.lst-kix_3uayykrrfdcf-3{list-style-type:none}.lst-kix_iixp2sb6ta62-3 > li:before{content:"- "}ol.lst-kix_dbkwut90ew6e-3.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-3 0}.lst-kix_xqyjtmw56zpv-0 > li:before{content:"(" counter(lst-ctn-kix_xqyjtmw56zpv-0,lower-latin) ") "}ul.lst-kix_khg6n6s9yryv-0{list-style-type:none}.lst-kix_w2guo1798a7q-8 > li:before{content:"- "}.lst-kix_xqyjtmw56zpv-3 > li{counter-increment:lst-ctn-kix_xqyjtmw56zpv-3}.lst-kix_xqyjtmw56zpv-6 > li:before{content:"" counter(lst-ctn-kix_xqyjtmw56zpv-6,lower-latin) ". "}ul.lst-kix_khg6n6s9yryv-8{list-style-type:none}ul.lst-kix_khg6n6s9yryv-7{list-style-type:none}ul.lst-kix_khg6n6s9yryv-6{list-style-type:none}ul.lst-kix_khg6n6s9yryv-5{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-1.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-1 0}ul.lst-kix_khg6n6s9yryv-4{list-style-type:none}ol.lst-kix_xqyjtmw56zpv-5.start{counter-reset:lst-ctn-kix_xqyjtmw56zpv-5 0}ul.lst-kix_khg6n6s9yryv-3{list-style-type:none}ul.lst-kix_khg6n6s9yryv-2{list-style-type:none}ol.lst-kix_5n2ou0hlvomq-8.start{counter-reset:lst-ctn-kix_5n2ou0hlvomq-8 0}ul.lst-kix_khg6n6s9yryv-1{list-style-type:none}.lst-kix_xqyjtmw56zpv-8 > li:before{content:"" counter(lst-ctn-kix_xqyjtmw56zpv-8,decimal) ". 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0}ol.lst-kix_xqyjtmw56zpv-7{list-style-type:none}ol.lst-kix_dbkwut90ew6e-1.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-1 0}ol.lst-kix_xqyjtmw56zpv-4{list-style-type:none}ol.lst-kix_xqyjtmw56zpv-5{list-style-type:none}ol.lst-kix_ll3ulrdzmx5d-4.start{counter-reset:lst-ctn-kix_ll3ulrdzmx5d-4 0}.lst-kix_xqyjtmw56zpv-4 > li:before{content:"" counter(lst-ctn-kix_xqyjtmw56zpv-4,lower-roman) ") "}ol.lst-kix_97b6r4n2nnjf-7{list-style-type:none}.lst-kix_9yokpth8l7z2-7 > li:before{content:"- "}ol.lst-kix_97b6r4n2nnjf-8{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-5{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-6{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-3{list-style-type:none}ol.lst-kix_xqyjtmw56zpv-4.start{counter-reset:lst-ctn-kix_xqyjtmw56zpv-4 0}ol.lst-kix_97b6r4n2nnjf-2.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-2 0}ol.lst-kix_97b6r4n2nnjf-4{list-style-type:none}.lst-kix_xqyjtmw56zpv-2 > li:before{content:"(" counter(lst-ctn-kix_xqyjtmw56zpv-2,decimal) ") "}.lst-kix_khg6n6s9yryv-6 > li:before{content:"- "}ol.lst-kix_5n2ou0hlvomq-6.start{counter-reset:lst-ctn-kix_5n2ou0hlvomq-6 0}.lst-kix_khg6n6s9yryv-4 > li:before{content:"- "}.lst-kix_khg6n6s9yryv-8 > li:before{content:"- "}.lst-kix_khg6n6s9yryv-5 > li:before{content:"- "}.lst-kix_xqyjtmw56zpv-0 > li{counter-increment:lst-ctn-kix_xqyjtmw56zpv-0}.lst-kix_x4vq44w6jjzx-1 > li:before{content:"- "}.lst-kix_khg6n6s9yryv-7 > li:before{content:"- "}ol.lst-kix_ll3ulrdzmx5d-1.start{counter-reset:lst-ctn-kix_ll3ulrdzmx5d-1 0}.lst-kix_x4vq44w6jjzx-0 > li:before{content:"- "}.lst-kix_x4vq44w6jjzx-5 > li:before{content:"- "}ol.lst-kix_97b6r4n2nnjf-6.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-6 0}.lst-kix_x4vq44w6jjzx-3 > li:before{content:"- "}.lst-kix_dbkwut90ew6e-4 > li{counter-increment:lst-ctn-kix_dbkwut90ew6e-4}.lst-kix_ll3ulrdzmx5d-7 > li{counter-increment:lst-ctn-kix_ll3ulrdzmx5d-7}.lst-kix_x4vq44w6jjzx-2 > li:before{content:"- "}.lst-kix_x4vq44w6jjzx-6 > li:before{content:"- 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"}.lst-kix_5n2ou0hlvomq-8 > li:before{content:"" counter(lst-ctn-kix_5n2ou0hlvomq-8,decimal) ". "}.lst-kix_temc2asnmng8-7 > li:before{content:"○ "}.lst-kix_dbkwut90ew6e-8 > li{counter-increment:lst-ctn-kix_dbkwut90ew6e-8}ol.lst-kix_ll3ulrdzmx5d-0.start{counter-reset:lst-ctn-kix_ll3ulrdzmx5d-0 0}.lst-kix_5n2ou0hlvomq-5 > li:before{content:"" counter(lst-ctn-kix_5n2ou0hlvomq-5,decimal) ") "}.lst-kix_temc2asnmng8-4 > li:before{content:"○ "}.lst-kix_temc2asnmng8-8 > li:before{content:"■ "}ol.lst-kix_97b6r4n2nnjf-5.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-5 0}ul.lst-kix_w2guo1798a7q-0{list-style-type:none}.lst-kix_temc2asnmng8-5 > li:before{content:"■ "}.lst-kix_5n2ou0hlvomq-6 > li:before{content:"" counter(lst-ctn-kix_5n2ou0hlvomq-6,lower-latin) ". 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"}.lst-kix_dbkwut90ew6e-1 > li{counter-increment:lst-ctn-kix_dbkwut90ew6e-1}.lst-kix_9yokpth8l7z2-0 > li:before{content:"- "}.lst-kix_97b6r4n2nnjf-4 > li{counter-increment:lst-ctn-kix_97b6r4n2nnjf-4}.lst-kix_9yokpth8l7z2-4 > li:before{content:"- "}ul.lst-kix_pjtr9kuz4bg1-0{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-1{list-style-type:none}.lst-kix_9yokpth8l7z2-2 > li:before{content:"- "}.lst-kix_9yokpth8l7z2-6 > li:before{content:"- "}ul.lst-kix_pjtr9kuz4bg1-8{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-6{list-style-type:none}ol.lst-kix_97b6r4n2nnjf-8.start{counter-reset:lst-ctn-kix_97b6r4n2nnjf-8 0}ul.lst-kix_pjtr9kuz4bg1-7{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-4{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-5{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-2{list-style-type:none}ul.lst-kix_pjtr9kuz4bg1-3{list-style-type:none}ul.lst-kix_iixp2sb6ta62-0{list-style-type:none}ul.lst-kix_iixp2sb6ta62-2{list-style-type:none}ul.lst-kix_iixp2sb6ta62-1{list-style-type:none}.lst-kix_9yokpth8l7z2-8 > li:before{content:"- "}ul.lst-kix_iixp2sb6ta62-8{list-style-type:none}ul.lst-kix_iixp2sb6ta62-7{list-style-type:none}ol.lst-kix_dbkwut90ew6e-8.start{counter-reset:lst-ctn-kix_dbkwut90ew6e-8 0}.lst-kix_xqyjtmw56zpv-3 > li:before{content:"" counter(lst-ctn-kix_xqyjtmw56zpv-3,lower-latin) ") "}ul.lst-kix_iixp2sb6ta62-4{list-style-type:none}ul.lst-kix_iixp2sb6ta62-3{list-style-type:none}ul.lst-kix_iixp2sb6ta62-6{list-style-type:none}ul.lst-kix_iixp2sb6ta62-5{list-style-type:none}

Chapter 7 Notes

  • Properties of a normal distribution(7.1)
  • The normal curve is symmetric about its mean M.(true) the normal curve is a symmetric distribution w/ one peak, which means mean = median = mode
  • The area under the normal curve to the right of M = ½
  • The points at x = M-O and x = M+O are the inflection points on the normal curve
  • Identify M+O

M = 18         O = 3

  • Applications of the normal distribution (7.2)
  • determine the area
  1. Area ← left Z=-0.52 = 0.3015

normaCDF (-, -0.52,0,1)

  1. ← left z=1.73 = 0.9582

normCDF(-,1.72, 0,1)

  1. ← left z=-1.72 = 0.0427

Determine the area

  1. ← left z=0.54 = 0.7054

  1. → right z=-0.84 = 0.7995

normCDF(-0.84, , 0,1)

  1. → right z=-1.32 = 0.9066

Determine the area

  1. → right z=0.47 = 0.3192
  2. → right z=0.45 = 0.3264

  1. z=-0.08+0.08/normCDF(-0.08,0.08,0,1)/=0.0638
  2. z=-2.21+0=0.4864

Find the z-score

  1. z=1.78+2.23=0.0247

        

  1. Normal curve ← left is 0.26

invnorm(0.26,0,1)=0.64

  1. Normal curve → right is 0.44

invnorm(0.44,0,1)=-0.15 to the right =0.15

  1. Separate middle 96% of distribution

        z-score invnorm(0.02,0,1)=-2.05,205

  1. Separate middle 79% of distribution

 invnorm(0.105,0,1)=-1.25 -1.25,1.25We also discuss several other topics like What happens if an antimicrobial drug has a high selective toxicity?

Find the value of Zoc

  1. Z0.17 1-0.17=0.88 invnorm(0.83,0,1)=0.95
  2. Z0.18 1-0.18=082 invnorm(0.82,0,1)=0.92
  • p(x>42) M=40 O=7

normCDF(42,,50,7)=0.8735

  • P(x<39) M=46 O=7

normCDF(-,39,46,7)=0.1587

  • P(35<x<64) M=50 O=7

normCDF(35,64,50,7)=0.9612

  • Assume x is normally distributed. M=59 O=7

Find the 14th percentileDon't forget about the age old question of governors (so why, trump, would they rig it for a democrat?

14th percentile = 0.14 invnorm(0.14,59,7)=51.44

  • Find the 11th percentile M=54 O=7

invnorm(0.11,54,7)=45.41

  • 86th percentile M=50 O-7

invnorm(0.86,50,7)=57.56

  • Find probability

Probability <60.1 M=64.2 O=2.7We also discuss several other topics like Why is it important to study Ethnicity?

normCDF(-,60.1,64.2,2.7)=0.06442

probability<60 M=63.5 O=2.6We also discuss several other topics like How is physical amplitude related to perceptual loudness?

normCDF(-,60,63,2.6)=0.0891Don't forget about the age old question of What is testing to know whether software is using more power?
We also discuss several other topics like shannon jette umd

Assessing normality(7.3

  • A normal probability plot is  graph that plots observed data versus normal scores
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