# Forward Normal Problems

• What's the probability?
• Know observed value
• Z-score -> percentiles

# Backward Normal Problems

• What's the observed value
• Know probability
• Persentiles -> z-score
• observed = mean + z standard deviation

# When will we see people of negative height?

• Mean height of a grown American men: 1.776m(5ft10in)
• SD: 9.6cm(3.78in)
• Is there any people with negative height?
• z-score of 0? (-18.5)

# What's the percentile of -18.5?

• How small is it?
• We have 70 billion people in the world now
• We can assume even larger, there are 107.6 people ever lived on earth
• exist one's probability is

# How many people will generate a negative height person?

• 95% confidence is
• 29 thousand billion billion billion billion billion billion billion billion people!
• How large is it?
• a computer of the current generation, it would need years to count this number.
• Much longer than the age of the earth.

# However, it is impossible

• Essentially, all models are wrong, but some are useful. -- George E. P. Box
• This artile is written by Patrik Perlman, Significance, feb. 2013, 46-48