The table displays the number of butterflies collected in a sample over three years. What inferences can be made from the sample
2 answers:
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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.
Answer:
Step-by-step explanation:
By definition, the perimeter of a rectangle is:
Where "l" is the lenght and "w" is the width.
If you solve for "l":
In this case, you know that the following expression represents the perimeter of the rectangle:
And the width of that rectanle is represented wih this expression:
Therefore, based on the explained above, you can conclude that the lenght of that rectangle is given by:
Finally, simplifying the expression, you get:
The limit of the expression as x approaches -3 is -24
<h3>How to determine the limit of the expression?</h3>The expression is given as:
As x approaches -3.
The limit expression becomes
Substitute -3 for x in the expression
Evaluate the expression
Hence, the limit of the expression as x approaches -3 is -24
Read more about limit expressions at:
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