lecture8 - 2 1 Normal Distribution 2 Binomial Distribution...

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1. Normal Distribution Given: μ = mean; σ = standard deviation; = infinity; 1.1. Probability of X less than a . P [ X < a ] = normCDF ( -∞ , a, μ, σ ) 1.2. Probability of X less than or equal a . P [ X a ] = normCDF ( -∞ , a, μ, σ ) 1.3. Probability of X at most a . P [ X a ] = normCDF ( -∞ , a, μ, σ ) 1.4. Probability of X no more than a . P [ X a ] = normCDF ( -∞ , a, μ, σ ) 1.5. Probability of X greater than a . P [ X > a ] = normCDF ( a, , μ, σ ) 1.6. Probability of X greater than or equal to a . P [ X a ] = normCDF ( a, , μ, σ ) 1.7. Probability of X at least a . P [ X a ] = normCDF ( a, , μ, σ ) 1.8. Probability of X no less than a . P [ X a ] = normCDF ( a, , μ, σ ) 1.9. Probability of X between a & b , exclusive. P [ a < X < b ] = normCDF ( a, b, μ, σ ) 1.10. Probability of X between a & b , inclusive. P [ a X b ] = normCDF ( a, b, μ, σ ) 1.11. Find a given the lower probability. P [ X < a ] = percentile ; a = invnorm ( percentile, μ, σ ) 1.12. Find a given the upper prob. P [ X > a ] = upperProb ; P [ X a ] = 1 - upperProb. ; a = invnorm ((1 - upperProb ) , μ, σ ) 1 2 2. Binomial Distribution Given: n = sample size, p = probability of an event, a = number of successes.
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