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. What is the expected temperature?

Answer 1

Thank you for posting your question here at brainly. 

a.) What is the probability that the temperature will be above 21∘? 

The density function f(x) is 

f(x) = 1/20 for 15 < x < 35 and 0 otherwise. 

a) 
P(x > 21) = 1 - P(x < 21) 
  = 1 - integral from 15 to 21 of (1/20) dx = 1 - (6/20) = 7/10. 

b.) What is the probability that the temperature will be between 19∘ and 33∘?

b) 
P(19 < x < 33) = P(x < 33) - P(x < 19)