Mathematics, 21.02.2020 04:45 kaiya2022547

A large electronic office product contains 2000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.995, and assume that the components fail independently. Approximate the probability that 5 or more of the original 2000 components fail during the useful life of the product.
(apply the ±½ correction factor and round value of standard normal random variable to 2 decimal places.) Round your answer to four decimal places (e. g. 98.7654).

Answers: 3

Show answers

Answers

Answer from: Alex9089435028

$P(\geg 5)= P(X 4.5)$

We can use the z score formula given by:

$z= \frac{x-\mu}{\sigma}$

And using this formula we have:

$P(X4.5) = P(Z\frac{4.5-10}{0.224}) =P(Z-24.60)$

And using the complement rule we have this:

P(Z24.60)= 1-P(Z

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=2000, p=1-0.995= 0.005)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X\geq 5)$

For this case since we have independence and the following two conditions:

$np = 2000*0.005 = 10 \geq 10[/tx][tex] n(1-p) = 2000*(1-0.005)= 1990 \geq 10$

We can use the normal approximation from the binomial distribution, and the mean would be given by:

$\mu = np =2000*0.005= 10$

$\sigma = \sqrt{np(1-p)}= \sqrt{2000*0.005(1-0.005)}= 0.224$

And using the continuity correction factor we have this:

$P(\geg 5)= P(X 4.5)$

We can use the z score formula given by:

$z= \frac{x-\mu}{\sigma}$

And using this formula we have:

$P(X4.5) = P(Z\frac{4.5-10}{0.224}) =P(Z-24.60)$

And using the complement rule we have this:

P(Z24.60)= 1-P(Z

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

x coordinate is none

step-by-step explanation:

Another question on Mathematics

Mathematics, 20.06.2019 18:02

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 15.

Answers: 1

Answer

Mathematics, 21.06.2019 15:00

Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

Draw a tape diagram to represent each situation.for some of the situations,you need to decide what to represent with a variable andre bakes 9 pans of brownies.he donates 7 pans to the school bake sale and keeps the rest to divide equally among his class of 30 students

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

To decrease an amount by 16% what single multiplier would you use

Answers: 1

Answer

You know the right answer?

A large electronic office product contains 2000 electronic components. Assume that the probability t...

Questions

Mathematics, 08.10.2019 01:00

Triangle abc with segment bd where point d is between points c and a, bc equals x, bd equals y, cd equals w, da equals z, and ba equals v what express...

Mathematics, 08.10.2019 01:00