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

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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) 

Answer 2

Using the uniform distribution, it is found that the expected temperature is of 25 ºF.

What is the uniform probability distribution?

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The expected value is given by:

$E(X) = \frac{a + b}{2}$

In this problem, the low temperature for each day of the month tend to have a uniform distribution over the interval 15∘ to 35 ∘F, hence a = 15, b = 35.

Then, the expected value is of:

$E(X) = \frac{a + b}{2} = \frac{15 + 35}{2} = 25$

More can be learned about the uniform distribution at https://brainly.com/question/13889040