PC Labs for SO5041: Week 5

Table of Contents

Week 5 Lab: the Normal Distribution

Normal Distribution

Table 1: Table of the Standard Normal Distribution: Right tail (probability of X>z)
  0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
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

Note: As an alternative to the printed table, use the following app: http://teaching.sociology.ul.ie:3838/apps/snd/

Using the following app: https://teaching.sociology.ul.ie/apps/snd/ or table 1, answer the following questions:

  • 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?

Working backwards

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: