Question 9 of 10

The number of flaws in a fiber optic cable follows a Poisson distribution. It is known that the mean number of flaws in 50m of c

boyakko [2]

Answer:

(a) The probability of exactly three flaws in 150 m of cable is 0.21246

(b) The probability of at least two flaws in 100m of cable is 0.69155

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is 0.13063

Step-by-step explanation:

A random variable X has a Poisson distribution and it is referred to as Poisson random variable if and only if its probability distribution is given by

$p(x;\lambda)=\frac{\lambda e^{-\lambda}}{x!}$ for x = 0, 1, 2, ...

where $\lambda$ , the mean number of successes.

(a) To find the probability of exactly three flaws in 150 m of cable, we first need to find the mean number of flaws in 150 m, we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 150 m of cable is $1.2 \cdot 3 =3.6$

The probability of exactly three flaws in 150 m of cable is

$P(X=3)=p(3;3.6)=\frac{3.6^3e^{-3.6}}{3!} \approx 0.21246$

(b) The probability of at least two flaws in 100m of cable is,

we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 100 m of cable is $1.2 \cdot 2 =2.4$

$P(X\geq 2)=1-P(X$

$P(X\geq 2)=1-p(0;2.4)-p(1;2.4)\\\\P(X\geq 2)=1-\frac{2.4^0e^{-2.4}}{0!}-\frac{2.4^1e^{-2.4}}{1!}\\\\P(X\geq 2)\approx 0.69155$

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is

$P(X=1)=p(1;1.2)=\frac{1.2^1e^{-1.2}}{1!}\\P(X=1)\approx 0.36143$

The occurrence of flaws in the first and second 50 m of cable are independent events. Therefore the probability of exactly one flaw in the first 50 m and exactly one flaw in the second 50 m is

$(0.36143)(0.36143) = 0.13063$

4 0

1 year ago

A gallon of stain is enough to cover 200 square feet of decking. Bradley has two areas of decking he would like to cover with st

Margaret [11]

He needs at least 2 gallons of the stain; though he will not use all of the second gallon

4 0

1 year ago

Read 2 more answers

A referendum failed by a vote of 36 No's and 24 Yes's. To make a pie chart of this result, what is the lesser measure in degrees

Daniel [21]

From the given number of people who voted Yes and No to the referendum, there are 60 people all in all. The fewer of which is 24 which voted as Yes. If we are to construct a pie chart and calculate the measure of the smaller angle, we take the ratio of 24 and 60 and multiply it to 360.

measure of angle ACB = (24/60)(360)
measure of angle ACB = 144°

Thus, the angle measure 144°.

3 0

1 year ago

Jessica deposits $5,000 at the end of each year in an account earning 2.45% interest, compounded annually. What is the future va

denpristay [2]

Hi there
If the amount deposited at (end) of each year, use the formula of the (future/present) value of annuity ordinary

If the amount deposited at the (beginning) of each year use the formula of the (future/present) value of annuity due

So
FvAo=5,000×(((1+0.0245)^(5)−1)
÷(0.0245))
=26,255.38...answer

Hope it helps

8 0

1 year ago

How many terms in the arithmetic sequence(2,4,6,8....) will give sum of 600

andriy [413]

Answer:

24 terms

Step-by-step explanation:

The sum of an arithmetic sequence is the average of the first and last terms, multiplied by the number of terms. The last term is given by ...

an = a1 + (n-1)d

We have a sequence with first term a1 = 2 and common difference d = 2. So the last term is ...

an = 2+ 2(n -1) = 2n

Then the average of first and last terms times the number of terms is ...

Sn = 600 = n(2 + 2n)/2 = n(n+1) . . . . . . close to n²

We can solve the quadratic in n, or we can estimate the value of n as the integer just below the square root of 600.

√600 ≈ 24.5

so we believe n = 24.

_____

<em>Check</em>

S24 = 24·25 = 600 . . . . . . as required.

8 0

1 year ago