The table below shows the number of e-mails received each day by a

An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the

lora16 [44]

Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

4000 if the device fails during the first year. The amount of the

benefit decreases by 1000 each successive year until it reaches 0.

If the device has not failed by the beginning of any given year, the

probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x 4000 3000 2000 1000 0

P(x) 0.4 0.6×0.4 0.6² × 0.4 0.6³ × 0.4 1 - 0.8704

(0.4) (0.24) (0.144) (0.0864) (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

= 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

= 1600 + 720 + 288 + 86.4 + 0

= 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

5 0

2 years ago

The line passing through (-2,5) and (2,p) has a gradient of -1/2. <br><br> Fnd the value of p

makkiz [27]

Given:

The line passing through (-2,5) and (2,p) has a gradient of $-\dfrac{1}{2}$ .

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

The line passing through (-2,5) and (2,p). So, the slope of the line is:

$m=\dfrac{p-5}{2-(-2)}$

$m=\dfrac{p-5}{2+2}$

$m=\dfrac{p-5}{4}$

It is given that the gradient or slope of the line is $-\dfrac{1}{2}$ .

$\dfrac{p-5}{4}=-\dfrac{1}{2}$

On cross multiplication, we get

$2(p-5)=-4(1)$

$2p-10=-4$

$2p=-4+10$

$2p=6$

Divide both sides by 2.

$p=3$

Therefore, the value of p is 3.

4 0

2 years ago

If you bought a set of markers for $2.85 and paid for it with a 5 dollar bill, how much change would you receive?

miss Akunina [59]

3.15 dollar you gonna get back

4 0

2 years ago

Read 2 more answers

Shannon's family is going to install a custom swing set in the backyard. There are 5 kinds of swings and 3 kinds of slides, and

asambeis [7]

Answer:

15 different swing sets

Step-by-step explanation:

The swing set is composed by one swing and one slide.

There is 5 different types of swing, so there are 5 possibilities to fill the one swing we need.

There are 3 different types of slides, so there are 3 possibilities to fill the one slide we need.

So, to find the total number of swing sets, we just need to multiply the swing possibilities and the slide possibilities:

Number of sets = 5 * 3 = 15 different sets

8 0

3 years ago

Pinto is planning to paint the walls of a bedroom that is 20 feet long, 15 feet wide, and 8 feet high. Is he too has 1 gallon of

eimsori [14]

Answer:

0.4 gallons

Step-by-step explanation:

Length of a bedroom= 20 feet

Breadth of a bedroom= 15 feet

Height of a bedroom= 8 feet

Area of walls of a bedroom= 2(l+b)×h

Area of walls of a bedroom=2(20+15)×8 $ft^{2}$

Area of walls of a bedroom= 2× 35×8 $ft^{2}$

Area of walls of a bedroom=560 $ft^{2}$

Amount of paint in 1 gallon = 400 $ft^{2}$

Number of gallons required= $\frac{560}{400}$

Number of gallons required= 1.4 gallons

Hence, 0.4 extra gallons required

5 0

3 years ago