two simple math questions
1. Human IQ scores are approximately normally distributed with mean 100 and standarddeviation 15. Determine the minimum IQ scores for the top 5% of the population.
2. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H),
with probabilities 0.1, 0.3, and 0.6 respectively. A lab test was then taken from thepatient. Past tests on similar patients show the following conditional probabilities on thetest result being positive (+), neutral (0), or negative (-):
P(+|F) = 0.8 P(0|F) = 0.1 P(-|F) = 0.1P(+|C) = 0.2 P(0|C) = 0.7 P(-|C) = 0.1P(+|H) = 0.1 P(0|H) = 0.3 P(-|H) = 0.6
Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given thata +, 0, or – test result has been observed.
