Question

A company advertises that their plastic concrete framework can be used 300 times in casting before it starts to deteriorate. The probability that their product can sustain up to 350 of casting is given in the following formula. Find the probability that the frameworks can last up to 350 times by using the Simpson’s 3/8 rule with n= 300

Answer 1

To find the probability that the frameworks can last up to 350 times using Simpson’s 3/8 rule with n = 300, divide the range into equal subdivisions, calculate the width of each subdivision, evaluate the function at each subdivision point, and sum up the multiplied values.

Step-by-step explanation:

To find the probability that the frameworks can last up to 350 times using Simpson’s 3/8 rule with n = 300, we first need to understand the concept behind Simpson's 3/8 rule. Simpson's 3/8 rule is a numerical integration method used to approximate the area under a curve.

1. Divide the range of integration (0 to 350) into n (300) equal subdivisions.
2. Calculate the width of each subdivision, h, by dividing the range by n.
3. Evaluate the function at each subdivision point and multiply the function value at the endpoints by 1, the function value at the interior points by 3, and the function value at points that are multiples of 3 by 2.
4. Sum up these multiplied values and multiply the sum by the width of each subdivision, h/8.

The result of this calculation will give you the probability that the frameworks can last up to 350 times. It's important to note that this method is an approximation and may not be 100% accurate.