Stats Help Homework

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 181-cm and a standard deviation of 0.8-cm.

Find P₆₁, which is the length separating the shortest 61% rods from the longest 39%.

Answer 1

P₆₁ = mean + z × std deviation

Where:

1. mean = 181 cm
2. std deviation = 0.8 cm

Steps:

1. Find z-score for P₆₁: The z-score corresponding to 61% (or 0.61) is roughly 0.31.
2. Use z-score to find P₆₁:

P₆₁ = 181 + (0.31 × 0.8) P₆₁ = 181 + 0.248 P₆₁ = 181.248 cm

So, P₆₁ is approximately 181.248 cm.