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The annual precipitation amounts for Iowa appear to be normally distributed with a mean of 32.473...

The annual precipitation amounts for Iowa appear to be normally distributed with a mean of 32.473 inches and a standard deviation of 5.601 inches.

(a)If one year is randomly selected, find the probability that the annual precipitation is less than 29.000 inches.

(b)If a decade of 10 years is randomly selected, find the probability that the annual precipitation amounts have a mean less than 29.000 inches.

(c) Why is the probability in part (b) smaller than the probability for part (a)? Explain.

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