Records indicate that the daily high January temperatures on a tropical island tend to have a uniform distribution over the interval from 75°F to 90°F. A tourist arrives on the island on a randomly selected day in January. a. What is the probability that the temperature will be above 80°F
b. What is the probability that the temperature will be between 80°F and 85°F 
c. What is the expected temperature?

a) 0.6667 = 66.67% probability that the temperature will be above 80°F.

b) 0.3333 = 33.33% probability that the temperature will be between 80°F and 85°F.

c) The expected temperature is of 82.5ºF.

Step-by-step explanation:

Uniform distribution:

The probability of all outcomes between a and b is the same.

Uniform distribution over the interval from 75°F to 90°F.

This means that

a. What is the probability that the temperature will be above 80°F?

We have that, on the uniform distribution:

In this question:

0.6667 = 66.67% probability that the temperature will be above 80°F.

b. What is the probability that the temperature will be between 80°F and 85°F?

We have that:

Then, in this question:

0.3333 = 33.33% probability that the temperature will be between 80°F and 85°F.

c. What is the expected temperature?

The expected value of the uniform distribution is:

In this question:

The expected temperature is of 82.5ºF.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: