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Sagot :
0.933 is approximate probability that x is less than 6.3 (round off to third decimal place).
What is Probability?
Calculating or estimating how likely or "possible" something is to occur is the subject of probability.
Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.
Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.
Given X₁,X₂, ............X₃₀₀ are IID random samples from Xi ~ Gamma ( shape = 3 scale = 2 ) . The mean and variance are
E(Xi) = 3 * 2 = 6
Var (Xi) = 3 * 2² = 12
According to CLT,
X = X₁ + X₂ + ............+ X₃₀₀/300
has approximately normal distribution X ~ N( 6,12/300) So the probability,
P( X < 6.3 ) = P( Z < 6.3 - 6/√12/300
P ( X < 6.3 ) = P( Z < 1.5 )
P (X < 6.3 ) = Ф (1.5 )
P (X < 6.3 ) = 0.933
Learn more about Probability
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