Question

The lengths of nails produced in a factory are normally distributed with a mean of 5.16 centimeters and a standard deviation of 0.04 centimeters. Find the two lengths that separate the top 8% and the bottom 8%.
____________________
Send me motivation quotes
best will be brainliest​

Answer 1

Answer:

5.10 cm and 5.22 cm

Explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score, \mu=mean,\ \sigma=standard\ deviation$

The top 8% corresponds with a z score of 1.41, Hence:

$1.41=\frac{x-5.16}{0.04} \\\\x-5.16=0.0564\\\\x=5.22\ cm$

The bottom 8% corresponds with a z score of -1.41. Hence:

$-1.41=\frac{x-5.16}{0.04} \\\\x-5.16=-0.0564\\\\x=5.10\ cm$

The lengths are 5.10 cm and 5.22 cm