K=0 ∑ 39 8(− 8 7 ) k ≈

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 means "a number n increased by 6.2"?

hichkok12 [17]

Answer:

n + 6.2

Step-by-step explanation:

Increased here means addition, addition of 6.2 with the number n.

8 0

3 years ago

Read 2 more answers

What error did anna make?

Lapatulllka [165]

Answer:

The last option

Step-by-step explanation:

she did not change the sign of +6 to -6

the constant term should be -15 and not -3

6 0

3 years ago

Find the 64th term in the number sequence 4,9,14,19

Karolina [17]

Answer:

319 is the term

Step-by-step explanation:

Please give me brainliest :)

8 0

2 years ago

Read 2 more answers

Find the quotient of and express it in the simplest form

nirvana33 [79]

Answer:

No answer can be found

Step-by-step explanation:

There isn't any value to find and express in simplest form lol.

5 0

3 years ago

K=0 ∑ 39 ​ 8(− 8 7 ​ ) k ≈

K=0 ∑ 39 8(− 8 7 ) k ≈