Question

The average high temperatures in Washington, DC vary by month. They are normally distributed and vary as follows:



· January: Average is 41 degrees with a standard deviation of 5 degrees.

· July: Average is 86 degrees with a standard deviation of 9 degrees.





Is it more likely to have a 51-degree day in January or a 104-degree day in July?

Answer 1

They’re equally likely.

For January: z = (51 − 41)/5 = 2.0.
For July: z = (104 − 86)/9 = 2.0.

A z of 2.0 gives an upper-tail probability ≈ 1 − Φ(2.0) ≈ 0.0228 (about 2.3%) for each event.