The mean daily rainfall in Los Angeles in December is 0.05 inches with a standard deviation of 0.02 inches. What is the probability that the total rainfall in Los Angeles for 37 randomly selected December days (possibly over several years) will not exceed 2 inches?
Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

The probability that the total rainfall will not exceed 2 inches is 0.8907.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

And the standard deviation of the distribution of the sum of values of X is given by,

As the sample size is large, i.e. n = 37 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of sample mean daily rainfall in Los Angeles.

Compute the probability that the total rainfall will not exceed 2 inches as follows:

Thus, the probability that the total rainfall will not exceed 2 inches is 0.8907.

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step-by-step explanation: