Question
In: Statistics and Probability
A weather forecaster predicts that the May rainfall in a local area will be between 2...
A weather forecaster predicts that the May rainfall in a local
area will be between 2 and 9 inches but has no idea where within
the interval the amount will be. Let x be the amount of
May rainfall in the local area, and assume that x is
uniformly distributed over the interval 2 to 9 inches.
(a) Calculate the expected May rainfall. (Round your answer to 1 decimal place.)
μx____ inches
(b) What is the probability that the observed May
rainfall will fall within two standard deviations of the mean?
Within one standard deviation of the mean? (Round all
intermediate and final answers to 4 decimal places.)
| Probability of May rainfall will fall within two SD | ||
| Probability of May rainfall will fall within one SD | ||
ps, the other answers with this same problem are wrong.
Solutions
Expert Solution
X ~ U (2,9)
a) µ = (2 + 9) / 2 = 5.5
sd = (9 - 2) / sqrt(12) = 2.021
b) P(within 2 sd) = P(5.5 - 2 * 2.021 < X < 5.5 + 2 * 2.201)
= P(1.098 < X < 9.902)
= P(2 < X < 9)
= 1
P(within 1 sd) = P(5.5 - 1 * 2.021 < X < 5.5 + 1 * 2.201)
= P(3.479 < X < 7.521)
= (7.521 - 3.479) / (9 - 2)
= 0.5774
orchestra answered 1 year agoRelated Solutions
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