A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 8.1 pounds and 13.1 pounds, respectively.

a.
Calculate the expected value and the standard deviation of this distribution. (Do not round intermediate calculations. Round your "Expected value" to 2 decimal places and "Standard deviation" answer to 4 decimal places.)

Expected value
Standard deviation
b.
Find the probability that the weight of a randomly selected bag is no more than 10.8 pounds. (Round your answer to 2 decimal places.)

Probability

c.
Find the probability that the weight of a randomly selected bag is at least 10.3 pounds. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Probability

(a) Expected value = 10.60

    Standard deviation = 1.4434

(b) The probability that the weight of a randomly selected bag is no more than 10.8 pounds is 0.54.

(c) The probability that the weight of a randomly selected bag is at least 10.3 pounds is 0.56.

Step-by-step explanation:

Let X =  the quantity of soil put in each bag.

The random variable X follows a Uniform distribution.

The range of the values of X are, [8.1, 13.1].

The probability density function of X is:

(a)

Compute the expected value of X as follows:

Thus, the expected value of X is 10.60.

Compute the standard deviation of X as follows:

Thus, the standard deviation of X is 1.4434.

(b)

Compute the probability that the weight of a randomly selected bag is no more than 10.8 pounds as follows:

Thus, the probability that the weight of a randomly selected bag is no more than 10.8 pounds is 0.54.

(c)

Compute the probability that the weight of a randomly selected bag is at least 10.3 pounds as follows:

Thus, the probability that the weight of a randomly selected bag is at least 10.3 pounds is 0.56.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

c.

step-by-step explanation: