Answer:
Step-by-step explanation:
From the given information:
Assuming we have an integer c to represent the components in the stocks.
Thus, the needed probability can be expressed as:
[tex]P(X_1+X_2+ ........ X_c \ge 2000)[/tex]
To break this down, we have:
[tex]P(\sum X_i \ge 2000) = P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )[/tex]
[tex]P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )= P (Z \ge 0.95 ) \ \ \ because \ Z_{0.05} = -1.65 \\ \\ \\ \dfrac{2000-100 n }{\sqrt{n \times 900}} = -1.65 \\ \\ \\ \dfrac{100\ n-2000 }{\sqrt{900n}} = 1.65 \\ \\ 100 n -1.65 \sqrt{900 n }-2000 = 0[/tex]
By solving the equation:
n = 23
Thus, relating to the needed condition; n ≥ 23
The needed number of the components that should be in stock should be at least 23.
