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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

3 years ago

Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second and two times the firs

Sav [38]

Answer:

first number= 19/5

second number= 2/5

Step-by-step explanation:

first number= a

second number= b

a+3b=5 equation 1

b+2a=8 equation 2

using equation 2 we have

b=8-2a

using equation 1 we have

a+3(8-2a)=5

a+24-6a=5

24-5=6a-a

19=5a

a=19/5 = first number

so using b=8-2a

we have

b=8-2(19/5)

b=8-(38/5)

b=2/5 = second number

4 0

3 years ago

Peach paint is 1 part yellow to 3 parts

katrin2010 [14]

Answer:

8/3

Step-by-step explanation:

3 parts yellow to 2 parts red

4 parts yellow to x parts red

x=4*2/3 =8/3 parts red.

If it is right then there you go

8 0

2 years ago

A random sample of n = 45 observations from a quantitative population produced a mean x = 2.5 and a standard deviation s = 0.26.

oee [108]

Answer:

P-value (t=2.58) = 0.0066.

Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean μ exceeds 2.4.

Then, the null and alternative hypothesis are:

$H_0: \mu=2.4\\\\H_a:\mu> 2.4$

The significance level is 0.05.

The sample has a size n=45.

The sample mean is M=2.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58$

The degrees of freedom for this sample size are:

$df=n-1=45-1=44$

This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t>2.5801)=0.0066$

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

7 0

3 years ago

Consider the lines y=8x+1, y=-8x+1 and y=2x+1. How are these lines the same, if at all? How do their slopes compare? Is there a

vivado [14]

Answer: the answer is blue

Step-by-step explanation:

8 0

2 years ago