A random number is selected from the interval [6.35, 10]. Find the probability that the number is within a distance of 0.25 from an even integer. (Answer as a decimal number, and round to 4 decimal places).

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Let

Xbe a random number selected from the interval. Then the probability density for the random variableXis8 and 10 are the only even integers that fit the given criterion (6 is more than 0.25 away from 6.35), so that we’re looking to compute

P(|

X– 8| < 0.25) + P(|X– 10| < 0.25)… = P(7.75 <

X< 8.25) + P(9.75 <X< 10.25)… = P(7.75 <

X< 8.25) + P(9.75 <X< 10)(since P(

X> 10) = 0)… = 0.2740 (8.25 – 7.75) + 0.2740 (10 – 9.75)

… =

0.2055