An example of a uniform distribution is x) or 0x The mean of the distribution fo

Question

An example of a uniform distribution is x) or 0x The mean of the distribution for this example is 0.5 and the standard deviation is approximately 0.29. The graph of the distribution for this example is a square ) with the height and width both equal to 1 unit. In general, the density function for a unifo m distribution on the inter al from a and x:) is given y . The mea is and hestandard deviation s a+b b- a (b-a) 12 Complete parts (a) through (c) below. (a) Verify that the area under the curve is 1. Choose the correct explanation below. 0 A. The area under the curve is a + b=0+1=1 B. The area under the curve is the area ofthe square, 1-1 = 1 ° C. The area under the curve is two times the mean, 2.0.5= 1. (b) Find the probability that x falls between 0.5 and 0.75 The probability s Type an integer or a decimal.) (c) Find the probability that x falls between 0.1 and 0.7 The probability is (Type an integer or a decimal.)

Explanation / Answer

a) Option B is correct.

b) P(0.5 < X < 0.75)

= (0.75 - 0.5)/(1 - 0)

= 0.25

c) P(0.1 < X < 0.7)

= (0.7 - 0.1)/(1 - 0)

= 0.60

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