Week 5 Lab

Normal Distribution

          Table of the Standard Normal Distribution
               Right tail (probability of X>z)
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        0.00  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09 
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 0.00| 0.500 0.496 0.492 0.488 0.484 0.480 0.476 0.472 0.468 0.464
 0.10| 0.460 0.456 0.452 0.448 0.444 0.440 0.436 0.433 0.429 0.425
 0.20| 0.421 0.417 0.413 0.409 0.405 0.401 0.397 0.394 0.390 0.386
 0.30| 0.382 0.378 0.374 0.371 0.367 0.363 0.359 0.356 0.352 0.348
 0.40| 0.345 0.341 0.337 0.334 0.330 0.326 0.323 0.319 0.316 0.312
 0.50| 0.309 0.305 0.302 0.298 0.295 0.291 0.288 0.284 0.281 0.278
 0.60| 0.274 0.271 0.268 0.264 0.261 0.258 0.255 0.251 0.248 0.245
 0.70| 0.242 0.239 0.236 0.233 0.230 0.227 0.224 0.221 0.218 0.215
 0.80| 0.212 0.209 0.206 0.203 0.200 0.198 0.195 0.192 0.189 0.187
 0.90| 0.184 0.181 0.179 0.176 0.174 0.171 0.169 0.166 0.164 0.161
 1.00| 0.159 0.156 0.154 0.152 0.149 0.147 0.145 0.142 0.140 0.138
 1.10| 0.136 0.133 0.131 0.129 0.127 0.125 0.123 0.121 0.119 0.117
 1.20| 0.115 0.113 0.111 0.109 0.107 0.106 0.104 0.102 0.100 0.099
 1.30| 0.097 0.095 0.093 0.092 0.090 0.089 0.087 0.085 0.084 0.082
 1.40| 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068
 1.50| 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056
 1.60| 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046
 1.70| 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037
 1.80| 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029
 1.90| 0.029 0.028 0.027 0.027 0.026 0.026 0.025 0.024 0.024 0.023
 2.00| 0.023 0.022 0.022 0.021 0.021 0.020 0.020 0.019 0.019 0.018
 2.10| 0.018 0.017 0.017 0.017 0.016 0.016 0.015 0.015 0.015 0.014
 2.20| 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.012 0.011 0.011
 2.30| 0.011 0.010 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.008
 2.40| 0.008 0.008 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.006
 2.50| 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005
 2.60| 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
 2.70| 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
 2.80| 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
 2.90| 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001
 3.00| 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
 3.10| 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
 3.20| 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
 3.30| 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
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Using this table, answer the following questions:

  1. Suppose you know that height of adult women in Ireland is normally distributed with mean 165cm and standard deviation 9cm:
    1. If you pick a woman at random, what is the chance she will be over 175cm?
    2. What proportion of women are less than 170cm?
    3. What is the chance a randomly chosen woman will be shorter than 150cm?
    4. What proportion of women are between 155cm and 160cm?
  2. In a particular class, exam scores are normally distributed with mean 65 and standard deviation 7:
    1. What score corresponds with the 95th percentile?
    2. What score corresponds with the 50th percentile?
    3. What score corresponds with the 25th percentile?

Online practice

Practice with the following online exercises:

  1. Proportion above X
  2. Proportion below X
  3. Proportion between two values

Brendan Halpin
Department of Sociology, University of Limerick
F1002, x 3147; brendan.halpin@ul.ie