# central limit theorem

for binomial distribution, B(n, p), defining Z = (X - μ)/σ, as n is tended to infinity,

the Z distribution approaches normal distribution, N(0, 1).

<Q>

the Capacities of 300 canned drinks almost obey normal distribution. the mean value is 199.3 g, the standard deviation 6.0 g.

What is the capacity of the 100th canned drink counting on from the larger number?

<A>

int_u^inf f(x) dx

by applying Z = (X - 199.3)/6.0

= int_v^inf g(z) dz = 1/3

finding v such that int_v^inf g(z) dz = 1/3,

v is 0.43 using normal distribution table.

solving (X - 199.3)/6.0 = 0.43 for X,

X = 201.88 (g)

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