SOLUTION: While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. a. What is the probability that

Question 1175124: While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection
that vary between 2.00 m and 7.00 m.
a. What is the probability that a randomly selected depth is less than 3.50 m?
b. What is the probability that a randomly selected depth is between 2.15 m and 5.50 m?
c. What is the expected value of the water depth?
d. What is the standard deviation of the water depth?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The range is 5 m and one goes from 2-3.5 m or 1.5 m
The probability is 1.5/5 or 0.30.
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The difference is 3.35 m and the probability is 3.35/5 or 0.67.
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expected value is midway between the two ends or 4.5 m
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the variance is (b-a)^2/12 or 25/12.
sd is sqrt of variance or 5/2 sqrt (3) or 5 sqrt(3)/6, or 1.44 m
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