Question

Suppose the maximum temperature T on any day in Brisbane in January follows a normal distribution with expectation 31 ◦C (degrees Celsius) and standard deviation 2 ◦C. Any temperature above 35 ◦C is deemed dangerous for older people. Using a ta- ble of the normal distribution or otherwise, find the probability that the temperature in Brisbane reaches a dangerous level on any day in January.

Suppose the expected temperature increases by an amount δ due to global warming, while the standard deviation remains the same. What is the smallest δ that will lead to a 5-fold increase in the probability from the previous question?

Instead of a table you may use R or Python to compute probabilities and quantiles. In R, use the functions pnorm and qnorm. In Python, you may use norm.cdf and norm.ppf, as in

     from scipy.stats import norm
     p = norm.cdf(2.0)      # probability
     q = norm.ppf(0.97725)  # quantile

Answer 1