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Lecture

MATH 1P98: Central Limit Theorem

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Department
Mathematics
Course
MATH 1P98
Professor
Dot Miners
Semester
Fall

Description
Central limit theorem Part 1: Suppose we have a distribution on x that appears to be normal (symmetrical at x-axis aka mean [µ], area beneath curve = 1, bell shaped curve). We can take a sample of size n for the distribution 1) x̄is also normal 2) the mean of the distribution is a µ σ 3) the standard deviation becomes σx̄= √ n Ex: Researchers found the height of wheat (x) follows a normal distribution, with µ = 0.9m and σ = 0.12m a) What’s the probability that a single wheat plant has a height between 0.85m and 0.82m? 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 = 0.23 b) What’s the probability that the mean height of 5 plants is between 0.85m and 0.82m? P(0.85 ≤ x̄≤ 0.82) µ
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