MATH 1P98 Lecture Notes - Central Limit Theorem, Standard Deviation

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P98
• Professor: Dot Miners

Document Summary

Part 1: suppose we have a distribution on x that appears to be normal (symmetrical at x-axis aka mean [ ], area beneath curve = 1, bell shaped curve). We can take a sample of size n for the distribution: x is also normal. 2) the mean of the distribution is a . 3) the standard deviation becomes x = . Ex: researchers found the height of wheat (x) follows a normal distribution, with = 0. 9m and . P(0. 85 x 0. 82) z1 = (0. 85-0. 9)/0. 12 = -0. 42 ; z2 = (0. 92-0. 9)/0. 12 = 0. 17. P(z 0. 17) p(z -0. 42) = 0. 5675 0. 3372. P(0. 85 x 0. 82) z1 = (0. 85 0. 9)/( ) = -0. 9316 ; z2 = (0. 92 0. 9)/( P(-0. 93 z 0. 37) = p(z 0. 37) p(z -0. 93) = 0. 6443 0. 1762. Part 2: x distribution is not known to be normal. In this case, we must have a sample size of at least 30. P(x > 56) z1 = (56 45)/(