Chapter 6: the Normal Distribution

Midterm II “Cheat Sheet”

/ For the normal distribution, you are either attempting to find P(-∞ to X) or P(-∞ to Z) given an X or Z value or
X or Z given P(-∞ to X) or P(-∞ to Z)
For the t distribution, you are also trying to find a probability or a value along the axis.
P(-∞ to X) = P(<X)
Population:
μ = mean; δ = standard deviation; π = proportion / Sample:
X = mean; S = standard deviation; p = proportion

For X

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For t

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For Z

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For p

P(<X) = NORMDIST(x,mean,sd,True) / P(<X) = TDIST(t,df,tails) / P(<Z) = NORMSDIST(Z) / P(<Z) = =NORMSDIST(Z)
X = NORMINV(P(<X),mean,sd) / t = TINV(P(<X),df) / Z = NORMSINV(P(<Z)) / Z = NORMSINV(P(<Z))

Chapter 6: The Normal Distribution

Changing X scale to Z scale:

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Changing Z scale to X scale

Z = (X-μ)/δ / X = μ+z δ

Chapter 7: Sampling and Sampling Distribution for the Mean

X Scale to find Xbar

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Z scale to find Xbar

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Z scale to find the mean proportion

σXbar = σ/√n / σXbar = σ/√n / σp = SQRT(π(1-π)/n)
Xbar = μ + Zσ/√n / Z = (Xbar – μ) / (σ/√n) / Z = (p-π) / SQRT(π(1-π)/n)

Chapter 8: Confidence Intervals

Confidence Interval of the Mean (σ Known)

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Confidence Interval of the Mean(σ Unknown, so use S))

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Confidence Interval of the Proportion

Xbar ± Zα/2 σ/√n
Zα/2 for 90% CI = 1.64
Zα/2 for 95% CI = 1.96
Zα/2 for 99% CI = 2.58 / Xbar ± tα/2 S/√n
Note; for TINV, the probability to enter is α, not α/2 / p ± Zα/2 SQRT(p (1-p)/n)

Estimating the required sample size (σ known)

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Estimating the required sample size (σ unknown)

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Estimating the required sample size (proportion)

n = Z2α/2 σ2 / e2 / NA / n = Z2α/2 (π (1- π) / e2

Chapter 5: Discrete Probability Distribution

Binomial Distribution

Binomial mean = np
Binomial δ= SQRT(nμ*(1-μ)) / Pnumber_s = BINOMDIST(number_s, trials, probability_s, FALSE)
Pnumber_s is the probability of a specific number of successes, not for P < a certain value.
Number_s = number of successes;
trials=number of trials,
probability_s = probability of success in a single trial

Poisson Distribution

/ Px = POISSON(x, mean, FALSE)
Px is the probability of a specific number of successes, not for P < a certain value.