Please full answer and explanation A sample distribution clo

Please full answer and explanation.

A sample distribution (closely approximating a normal distribution) of a critical part dimension has an average of 11.85 mm and a sample standard deviation of 1.33 mm. The lower specification limit is 11.41 mm. The upper specification limit is 12.83 mm. What percentage of parts will be produced below the lower specification limit of 11.41 mm?

Solution

Mean = u = 11.85
SD = 1.33

x = 11.41

z = (x - u) / SD

z = (11.41 - 11.85) / 1.33

z = -0.3308270676691729323308270676691729323308270676691729

We are interested in P(z < -0.3308270676691729323308270676691729323308270676691729)

Check this link ----> https://www.easycalculation.com/statistics/p-value-for-z-score.php

And since we need the percent that falls BELOW, we will look at the \"left tailed P-value\"

P(z < -0.3308270676691729323308270676691729323308270676691729) = 0.3704

Percentage answer ---> 0.3704 * 100

37.04% --> ANSWER