Mathematics, 14.02.2020 01:22 ellamai16

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 32% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below. a. Find the probability that both generators fail during a power outage (Round to four decimal places as needed.) b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Answers: 2

Show answers

Answers

Answer from: jayy1474

a) There is a 10.24% probability that both generators fail during a power outage.

b) There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

Step-by-step explanation:

For each emergency backup generator, there are only two possible outcomes. Either they work correctly, or they fail. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

In this problem we have that:

Assume that emergency backup generators fail 32% of the times when they are needed. So they work correctly 100-32 = 68% of the time. So p = 0.68

There are two generators, so n = 2

a. Find the probability that both generators fail during a power outage

This is P(X = 0)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.68)^{0}.(0.32)^{2} = 0.1024$

There is a 10.24% probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Either there are no working generators, or there is at least one working generator. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1024 = 0.8976$

There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

To be high enough for the hospital, this probability should be at least of 99%.

Answer from: Quest

sorry i dont know my friend

Give all angles of rotational symmetry less than 360°, listed from least to greatest.

Answer from: Quest

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)

Another question on Mathematics

Mathematics, 20.06.2019 18:04

Norma has an a-frame cabin. the back is shown below. how many square feet of paint will she need to cover the back of the cabin? explain how you found the answer.

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

You are cycling around europe with friends. a cycling festival is starting soon in barcelona. it will take 4.5 hours to cycle there. how many minutes in total is this?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Val and tony get paid per project. val is paid a project fee of $44 plus $12 per hour. tony is paid a project fee of $35 plus $15 per hour. write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.

Answers: 1

Answer

Mathematics, 22.06.2019 00:40

If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the canyon angle acb = 50° angle abc=100° a=75 yds what does c equal?

Answers: 1

Answer

You know the right answer?

Hospitals typically require backup generators to provide electricity in the event of a power outage....

Questions