The weather in Rochester in December is fairly constant. Records indicate that t
ID: 3366734 • Letter: 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
Answer
Ans ;low temerature for each day of month trend follow uniform distribution[15,35]
X=temperature ,f(x)=1/(b-a) ,where b=is upper value ,a=lower value so f(x)=1/20
(a) probability that the temperature is above 23 is =integration of f(x) from limit 23 to 35
=(1/20)[35-23]
=12/20
(b)probability that temperature will be lie between 17 to 30 =integration of f(x) from limit 17 to 30
=(1/20)[30-17]
=13/20
(c) Expected temperature =(a+b)/2
=(15+35)/2
=25
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