While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the probability that a randomly selected depth is within 1 standard deviation of the mean?
A)0.320
B)0.576
C)0.600
D)1.000

Question

Quizplus · Accepted Answer

The standard deviation of a uniform distribution is (b-a)/sqrt(12), where a and b are the minimum and maximum values, respectively. In this case, a = 2.00 m and b = 7.00 m, so the standard deviation is (7.00 m - 2.00 m)/sqrt(12) = 1.71 m. The mean of the distribution is (a + b)/2 = (2.00 m + 7.00 m)/2 = 4.50 m. Therefore, the probability that a randomly selected depth is within 1 standard deviation of the mean is P(4.50 m - 1.71 m < X < 4.50 m + 1.71 m) = P(2.79 m < X < 6.21 m) = 0.576.

While Conducting Experiments,a Marine Biologist Selects Water Depths from a Uniformly