An example of a uniform distribution is f x = 1 for 0sx 1. The mean of the distr

Question

An example of a uniform distribution is f x = 1 for 0sx 1. The mean of the distribution for this example is 0.5 and the standard deviation is approximately 0.29. The graph of the distribution or this example is a square with the height and width both equal to 1 unit. In general, the density function for a uniform distribution on the interval from x - a and xEb is given by f(x) - b-a The mean isand the standard deviation is ? a +b Complete parts (a) through (c) below. (a) Verify that the area under the curve is 1. Choose the correct explanation below. OA. The area under the curve is two times the mean, 2.0.5-1 O B. The area under the curve is ab 0+1-1 ° C. The area under the curve is the area of the square, 1·1-1. (b) Find the probability that x falls between 0.5 and 0.75. The probability is(Type an integer or a decimal.) (c) Find the probability that x falls between 0.1 and 0.6. The probability is(Type an integer or a decimal.)

Explanation / Answer

a) Option C is correct.

b) Probability = (0.75 - 0.50)/(1 - 0) = 0.25

c) Probability = (0.6 - 0.1)/(1 - 0) = 0.50

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