Answer:
75.8% probability that a 31 square foot metal sheet has at least 4 defects.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
In this problem, we have that:
3 defects per 18 square feet.
So for 31 square feet, we have to solve a rule of three
3 defects - 18 square feet
x defects - 31 square feet
So
Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.
Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.
So
We want
So
In which
So
Finally
75.8% probability that a 31 square foot metal sheet has at least 4 defects.