Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 216.5-cm and a standard deviation of 2.3-cm. For shipment, 24 steel rods are bundled together.

Find P₁₅, which is the average length separating the smallest 15% bundles from the largest 85% bundles.
P₁₅ = -cm

Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Given that, mean = 216.5 cm

standard deviation = 2.3 cm

sample size (n) = 24

We want to find, sample mean such that,

Therefore, we get

P_{​​​​​​15} = 216.01 cm