Question

1. A certain company makes electrical cables having a mean strength of 40 kg/cm² and a standard deviation of 2 kg/cm². Assuming the strength follows a normal distribution,

a. What percentage of cables will have a strength exceeding 43 kg/cm²?

b. If strength is measured to the nearest kg/cm², what percentage of cables will have

strength exceeding 43 kg/cm²?

c. Illustrate the normal curve for a and b.

Answer 1

a)

$$P(X>43)=1-P(Z\le\dfrac{43-40}{2})$$

$$=1-P(Z\le1.5)=0.0668$$

b)

$$P(X\ge43.5)=1-P(Z<\dfrac{43.5-40}{2})$$

$$=1-P(Z<1.75)=0.0401$$

c)

a)

b)