Explanation:
We can use the normal distribution to estimate the number of times there would be less than 42 mm of rainfall during August in Claudona over 20 years.
To do this, we need to find the Z-score for 42 mm using the formula: Z = (X - μ) / σ where X is the value we're interested in (42 mm), μ is the mean (48 mm), and σ is the standard deviation (6 mm). Z = (42 - 48) / 6 = -1 Using a Z-score table or calculator, we can find the probability of getting a Z-score less than -1, which represents the probability of getting less than 42 mm of rainfall in August in Claudona: P(Z < -1) = 0.1587
This means that about 15.87% of the time, we would expect there to be less than 42 mm of rainfall during August in Claudona.
To estimate the number of times this would happen over 20 years, we can multiply this probability by the number of years: 0.1587 * 20 = 3.174 Rounding to the nearest integer, we would expect there to be about 3 years over 20 with less than 42 mm of rainfall during August in Claudona.