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Rainfall The rainfall (in inches) in a certain region is uniformly distributed over the interval $[32,44] .$a. What is the expected number of inches of ruinfall?b. What is the probability that the rainfall will be between 38 and 40 in.?
(a) 38 inches $\qquad$ (b) $\frac{1}{6}$
Calculus 1 / AB
Chapter 18
Probability and Calculus
Section 3
Special Probability Density Functions
Continuous Functions
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Okay, so for this question, we're told it's got a uniform random variable between 32 44. We want to know what the mean or the expectation is s. That's gonna be halfway between these two, which is 38. And then we want to know the probability that X is between 38 and 40. And if we try this out so we can avoid doing any actual calculations, we see that this is 12 across. And if we did 38 40 it would be do across. So this can just be to over 12 which is 1/6. So these are our final answers.
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