This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 100 customer orders to fill. Each order requires one component part that is purchased froma supplier. However, typically, 2% of the components are identifiedas defective, and the components can be assumed to beindependent.a)If the manufacturer stocks 100 components, what is theprobability that the 100 orders can be filled without reorderingcomponents?b) If the manufacturer stocks 102 components, what is theprobability that the 100 orders can be filled without reorderingcomponents?c) If the manufacturer stocks 105 components, what is theprobability that the 100 orders can be filled without reorderingcomponents?

(a) 0.1326

(b) 0.2732

(c) 0.0410

Step-by-step explanation:

Let X = number of defective components.

The probability of X is, P (X) = p = 0.02.

The random variable X follows a Binomial distribution with parameters n and p. The probability mass function of a Binomial distribution is:

(a)

Compute the probability that the 100 orders can be filled without reordering components as follows:

n = 100

Thus, the probability that the 100 orders can be filled without reordering components is 0.1326.

(b)

Compute the probability that out of 102 orders 2 orders needs reordering as follows:

n = 102

Thus, the probability that out of 102 orders 2 orders needs reordering is 0.2732.

(c)

Compute the probability that out of 105 orders 2 orders needs reordering as follows:

n = 105

Thus, the probability that out of 105 orders 5 orders needs reordering is 0.0410.

Since the area of a rectangle is 20 square feet, the length of this rectangle is equal to 4 feet.

Given the following data:

To find the length of the rectangle:

Translating the word problem into an algebraic equation, we have;

  ....equation 1.

   ....equation 2.

Mathematically, the area of a rectangle is given by the formula;

   ...equation 3.

Substituting the values into the eqn. 2, we have;

L = -5 or L = 4

Length, L = 4 feet.

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