The probability density function shown models the amount of rainfall per year for a certain location. If the area of each square on the grid is 0.05, estimate the probability that the rainfall for the year is less than 8 inches.

Explanation:

The probability that the rainfall for the year is less than 8 inches is equal to the area under the curve of the probability density function to the left of 8 inches.

I attached a graph with the squares that cover that area in red.

There are 7 complete, or almost complete, red squares and 4 triangles.

For estimation purposes, you can count each triangle as half a square.

Thus, consider 7 + 4/2 = 7 + 2 = 9 squares.

Since the area of each square on the grid is 0.05, the area o 9 squares is:

Hence, your estimate of the probability that the rainfall for this year is less than 8 inches is 0.45.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true