Mathematics, 20.06.2021 16:30 zoelynn9104

The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent by a random variable x where repair time follow a normal distribution with mean 5 hour and standard deviation 1 hour , if 5 electrical breakdown ore randomly chosen , Find the probability that ( a all repaired time below 6 hours ( b ) exactly 3 of them repaired below 6 hours

Answers: 2

Show answers

Answers

Answer from: kassandramarie16

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that $\mu = 5, \sigma = 1$

This proportion is the p-value of Z when X = 6. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6 - 5}{1}$

Z = 1

Z = 1 has a p-value of 0.8413.

0.8413 repaired below 6 hours.

For the binomial distribution, this means that p = 0.8413

5 are chosen:

This means that n = 5

a) Probability that all are repaired in less than 6 hours

This is P(X = 5). So

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

$P(X = 5) = C_{5,5}.(0.8413)^{5}.(0.1587)^{0} = 0.4215$

0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) Probability that exactly 3 of them repaired below 6 hours

This is P(X = 3). So

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

$P(X = 3) = C_{5,3}.(0.8413)^{3}.(0.1587)^{2} = 0.15$

0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Answer from: Quest

i can answer this question sweetie!

step-by-step explanation:

Answer from: Quest

2/3

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Asalesperson earns $320 per week plus 8% of her weekly sales. the expression representing her earnings is 320 + 0.08x. which of the following describes the sales necessary for the salesperson to earn at least $1000 in the one week?

Answers: 2

Answer

Mathematics, 22.06.2019 01:00

Match the one-to-one functions with their inverse functions.

Answers: 1

Answer

Mathematics, 22.06.2019 01:50

Anew movie is released each year for 14 years to go along with a popular book series. each movie is 2 minutes longer than the last to go along with a plot twist. the first movie is 70 minutes long. use an arithmetic series formula to determine the total length of all 14 movies

Answers: 3

Answer

Mathematics, 22.06.2019 02:00

Hannah reads at a constant rate of 33 pages every 88 minutes. write an equation that shows the relationship between pp, the number of pages she reads, and mm, the number of minutes she spends reading.

Answers: 1

Answer

You know the right answer?

The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent b...

Questions