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.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

i think asking google will you get the answer to that question