Find the area of the rectangle in the picture

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago

Which percent is equivalent to 0.3? A. 0.003% B. 0.03% C. 3% D. 30%

Kitty [74]

Answer:

D, 30%

Step-by-step explanation:

you move the decimal point twice to the right

8 0

3 years ago

Read 2 more answers

How does the climate of the northeast affect the people/ animals/and plants that live there

Andru [333]

it is really cold so people will have to find food try to survive by hunting animals which is even more difficult also plants would barely get any water

3 0

3 years ago

Read the last sentence of "Ain't I a Woman?"

maxonik [38]

Answer:

They suggest that the audience has listened to and understood all of Truth’s reasons.

Step-by-step explanation:

Obliged to you for hearing me, and now old Sojourner ain’t got nothing more to say.

This Implies that she needs to say nothing more, because the truth was so blaringly obvious that everyone in the crowd understood it. It also implies that no better argument for her cause could be put forward, and none was needed.

7 0

2 years ago

Read 2 more answers

How many stamps that are 1.5 inches long and 1.5 inches wide will fit on a piece of paper that is 9 inches wide and one foot lon

Soloha48 [4]

Divide the paper which is 21 inches (12+9) by 1.5 and you have your answer which is 14

4 0

3 years ago