Ch. 5 Test Notes Probability Distributions: Requirements: ( ) 1p x∑ = (the sum of the ( )p x is between .99 and 1.01 due to rounding)

0 ( ) 1p x≤ ≤ (Each probability is between zero and one, including zero and one)

( )E x p x= ∑ 2 2 2( )x p xσ µ= ∑ −

( )x p xµ = ∑ 2σ σ=

Binomial Probabilities:

npµ = 2 (1 )np pσ = − (1 )np pσ = − Binomialpdf (n,p,x) the probability of getting x success with p (probability of success and n (number of trials) Binomialcdf (n,p,x) the probability of getting (at most ) x success with p (probability of success and n (number of trials). In other words, getting x or less than x successes. Probability of at least one success is always equal to 1- probability of no successes. P(at least one) = 1 – P(0) Normal Distributions: Normal cdf (Lower Limit, Upper limit, ,µ )σ gives the probabilities of the normal distribution (round answers to 3 significant digits) Z = invnorm (area left, 0,1) (round to 2 decimals) X = invnorm (area left, ,µ )σ (round to one decimal and include unit of measure)

xz µσ−

=