Question

1. In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution?

Answer 1

Using the empirical rule (≈95% within 2 standard deviations): 2σ = 89 − 86 = 3, so σ = 3/2 = 1.5°F.

(If you use the exact z-value 1.96 for 95%: σ = 3/1.96 ≈ 1.53°F.)