The weather in Rochester in December is fairly constant. Records indicate that t

Question

The weather in Rochester in December is fairly constant. Records indicate that the low temperature for each day of the month tend to have a uniform distribution over the interval 15? to 35?F. A business man arrives on a randomly selected day in December. (a) What is the probability that the temperature will be above 23?? answer: (b) What is the probability that the temperature will be between 17? and 30?? answer: (c) What is the expected temperature? answer: Give your answers exactly, or to at least 4 decimal places.

Explanation / Answer

X ~ Uniform (a,b) = Uniform ( 15 , 35)

a)

For P( X > x) = ( b - x) / ( b - a)

= (35-23) / ( 35 - 15)

= 0.60

b)

P( x1 < X < x2) = (x2 - x1) / ( b - a)

So,

P( 17 < X < 30) = ( 30 - 17) / ( 35 - 15)

= 0.65

c)

Expected value of uniform distribution = ( a + b) / 2

= ( 15 + 35 / 2)

= 25

Expected temperature = 25oF

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