(3 points) Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transpor…

Question

asked Feb 25, 2022 213k views

1 Answer

Fakingfantastic · Answer 1 · 2022-03-01T11:27:17+0000

Answer:

0.8743 = 87.43% probability that more than one accident occurs per year

Explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.

This means that
$\mu = 3.1$

What is the probability that more than one accident occurs per year?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

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

Then

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

P(X = 0) = (e^(-3.6)*(3.6)^(0))/((0)!) = 0.0273

P(X = 1) = (e^(-3.6)*(3.6)^(1))/((1)!) = 0.0984

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743$

0.8743 = 87.43% probability that more than one accident occurs per year