Central Limit Theorem-CLT. MM4D1. Using simulation, students will develop the idea of the central limit theorem. Central Limit Theorem - CLT.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
MM4D1. Using simulation, students will develop the idea of the central limit
Use to gain information about a sample mean
Use to gain information about an individual data value
1. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 ml. In fact, the contents vary according to a normal distribution with mean µ = 303 ml and standard deviation σ = 3 ml.
a) use z=(x-µ)/σ) & Table of negative Z-score
z=(300-303)/3 = -1
P(x<300) = 0.1587 or 15.87%,
b) P(x>300) = 1 – 0.1587 = 0.8413 or 84.13%
z=(300-303)/3 = -1 → P(x=300) = 0.1587
z=(310-303)/3 = 2.33 → P(x=310) = 0.9893
P(300<x<310) = 0.9893-0.1587 = 0.8306 or 83.06%
d) mean: 303, stdev: 3/sqrt(10) = 0.94868
e) z=(x-µ)/(σ/sqrt(10) & Table of negative Z-score
z=(300-303)/0.94868 = -3.16
p=0.0008 or 0.08%