Question

The weather in Rochester in December is tairty constant. Records indicate that the low temperature for each day of the month tend to have a unitorm 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 20∘ ?
(b) What is the probability that the temperature wal be between 20∘ and 26∘ ?
(c) What is the expected temperature?

Answer 1

The probability of the temperature being above 20∘ F is 0.75, the probability of the temperature being between 20∘ F and 26∘ F is 0.3, and the expected temperature is 25∘ F.

Step-by-step explanation:

To find the probability that the temperature will be above 20∘ F, we need to find the proportion of the interval from 20∘ F to 35∘ F in relation to the total interval from 15∘ F to 35∘ F. So, the probability is:

(35 - 20) / (35 - 15) = 15 / 20 = 0.75.

To find the probability that the temperature will be between 20∘ F and 26∘ F, we need to find the proportion of the interval from 20∘ F to 26∘ F in relation to the total interval from 15∘ F to 35∘ F. So, the probability is:

(26 - 20) / (35 - 15) = 6 / 20 = 0.3.

To find the expected temperature, we need to find the average of the low temperatures from 15∘ F to 35∘ F. So, the expected temperature is:

(15 + 35) / 2 = 25∘ F.