Topics 5-6 Business Statistics FCs
(straighterline) – Questions with Solved
Solutions
Mean - - A measure of central measurement that is computed by summing
all the values and dividing by the number of items. Commonly referred to as
an average or the expected value.
- Variance - - The arithmetic mean of the squared deviations of the
observations from the mean.
- Standard deviation - - The square root of the variance.
- Probability Distribution - - A listing of all the possible outcomes of an
experiment and the probability of each outcome occurring.
- Binomal probability distribution - - A probability distribution of outcomes
that will have only two possible values.
- Poisson Probability Distribution - - A discrete probability distribution that
involves tracking the number of times an event occurs over a period of time.
- Empirical Rule - - A rule that states that approximately 68% of the
distribution will be within + or - 1 standard deviation of the mean, 95% of the
distribution will be within + or - 2 standard deviations of the mean, and 99.7
of the distribution will be within + or - 3 standard deviations of the mean.
- Mean of a Probability Distribution Formula - - μ = ∑[xP(x)]
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
NOTE: use a table to calculate
- Variance of a Discrete Probability Distribution Formula - - σ² = Σ[ (x - μ)²
P(x) ]
σ² is the variance of the distribution
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
, NOTE: use a table to calculate
- Standard Deviation of a Discrete probability formula - - σ = square root of
Σ[ (x - μ)² P(x) ]
σ is the standard deviation of the distribution
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
NOTE: use a table to calculate
- Binomal Probability Distribution Formula - - P(x) = nCx π to power of x (1 -
π)to the power of n - x
P(x) is the probability of a value occurring
n is the number of observations
C is the desired combination
π is the probability of success on a single trial
x is the number of successes
NOTE: you can use Google Sheets to calculate
insert;function;binomdist
- Poisson Distribution Formula - - P(x) = (μ to the power of x)(e to the power
of -μ) / x!
P(x) is the probability of the event occurring
μ is the mean of the number of successes in an interval
e = 2.71828 (a numeric constant)
x is the number of successes
NOTE: use Google Sheets to calculate
insert;functions;poisson
=poisson(x,mean,cumulative)
put "0" for cumulative
- Mean of the Poisson (or Binomal) Probability Distribution Formula - - μ =
nπ
n is the number of trials
π is the probability of success on a single trial
- Converting to a Standard Normal Distribution Formula - - z = (X - μ) / σ
(straighterline) – Questions with Solved
Solutions
Mean - - A measure of central measurement that is computed by summing
all the values and dividing by the number of items. Commonly referred to as
an average or the expected value.
- Variance - - The arithmetic mean of the squared deviations of the
observations from the mean.
- Standard deviation - - The square root of the variance.
- Probability Distribution - - A listing of all the possible outcomes of an
experiment and the probability of each outcome occurring.
- Binomal probability distribution - - A probability distribution of outcomes
that will have only two possible values.
- Poisson Probability Distribution - - A discrete probability distribution that
involves tracking the number of times an event occurs over a period of time.
- Empirical Rule - - A rule that states that approximately 68% of the
distribution will be within + or - 1 standard deviation of the mean, 95% of the
distribution will be within + or - 2 standard deviations of the mean, and 99.7
of the distribution will be within + or - 3 standard deviations of the mean.
- Mean of a Probability Distribution Formula - - μ = ∑[xP(x)]
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
NOTE: use a table to calculate
- Variance of a Discrete Probability Distribution Formula - - σ² = Σ[ (x - μ)²
P(x) ]
σ² is the variance of the distribution
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
, NOTE: use a table to calculate
- Standard Deviation of a Discrete probability formula - - σ = square root of
Σ[ (x - μ)² P(x) ]
σ is the standard deviation of the distribution
μ is the mean of the probability distribution
∑ is sum
x is a value in the probability distribution
P(x) is a probability of a value in the distribution
NOTE: use a table to calculate
- Binomal Probability Distribution Formula - - P(x) = nCx π to power of x (1 -
π)to the power of n - x
P(x) is the probability of a value occurring
n is the number of observations
C is the desired combination
π is the probability of success on a single trial
x is the number of successes
NOTE: you can use Google Sheets to calculate
insert;function;binomdist
- Poisson Distribution Formula - - P(x) = (μ to the power of x)(e to the power
of -μ) / x!
P(x) is the probability of the event occurring
μ is the mean of the number of successes in an interval
e = 2.71828 (a numeric constant)
x is the number of successes
NOTE: use Google Sheets to calculate
insert;functions;poisson
=poisson(x,mean,cumulative)
put "0" for cumulative
- Mean of the Poisson (or Binomal) Probability Distribution Formula - - μ =
nπ
n is the number of trials
π is the probability of success on a single trial
- Converting to a Standard Normal Distribution Formula - - z = (X - μ) / σ
