Psych 2300 - Exam 2 questions well
answered graded A+ 2025/2026
z-score - ANS ✔✔a standard value that specifies the precise location of each X value (score)
within a distribution with reference to the SD
two purposes:
1) Identify the exact location of the original X value within the distribution
2) To form a standardized distribution that can be directly compared to other standardized
distributions
· A RAW score by itself does not provide much information about it's position within a
distribution
· Z-scores tell us exactly where your score is located in relation to EVERYBODY else
Two parts to a z-score
· The z-score transforms each X value into a signed value (+ or -)
· Note the z-score has two parts that are absolutely necessary - the SIGN and the VALUE
formula: z = (X - mean)/(standard deviation)
- numerator is a deviation score
- Denominator expresses deviation in standard deviation units
determining a raw score from a z-score - ANS ✔✔formula: X = m + z(standard deviation)
,using z-scores to standardize a distribution (purpose #2) - ANS ✔✔It is possible to transform
every X value in a distribution to z-scores - called a standardized distribution
standardized distribution - ANS ✔✔a distribution of scores that have been transformed to
create predetermined values for m (mean) and s (standard deviation) .
features of a standardized distribution - ANS ✔✔a) Shape - the shape of a standardized
distribution DOES NOT change from it's original shape
b) The Mean - standardized distributions ALWAYS have a mean of zero
c) Standard Deviation - standardized distributions always has an SD of 1
using z-scores for making comparisons - ANS ✔✔you cannot compare two exam scores from
different courses and really know anything about which course you're doing better in.
however, you can standardize both sets of distributions in order to make a comparison.
other standardized distributions based on z-scores - ANS ✔✔1. Using a Predetermined μ and σ
· Some distributions are famous for having predetermined values of μ and σ - such distributions
are computed to avoid negative values and decimals in the z-score
· Examples - IQ test and achievement test distributions
2. Two step process for transforming a distribution to predetermined values
a) Raw scores are transformed into z-scores
b) Z-scores are transformed into new X values so the specific mean and SD are attained
, probability - ANS ✔✔when several outcomes are possible, probability is the likelihood of any
particular outcome expressed in terms of a fraction or proportion.
formula: Probability of A = number of outcomes classified as A / total number of possible
outcomes
probability notation - ANS ✔✔notation: p(example) = the probability of the specific outcome
· Note - probability is defined as a proportion (fraction) - any probability question can be
restated as a proportion problem
· Note - probabilities range from 0 to 100
random sampling - ANS ✔✔requires the satisfaction of two requirements:
a) Each individual in the population must have an equal chance of being selected
- The "equal chance" requirement applies to individuals. Individual probabilities are combined
to find probabilities for groups.
b) If more than one individual is selected, there must be constant probability for each and every
selection
· Without replacing the selected sample - the rule of constant probability is violated
· Probability predicts samples not populations
probability and frequency distributions - ANS ✔✔Probability usually involves scores that can be
displayed in a frequency distribution graph
probability and the normal distribution - ANS ✔✔· Some things about the normal distribution
- It is symmetrical - what does this mean with respect to proportions?
answered graded A+ 2025/2026
z-score - ANS ✔✔a standard value that specifies the precise location of each X value (score)
within a distribution with reference to the SD
two purposes:
1) Identify the exact location of the original X value within the distribution
2) To form a standardized distribution that can be directly compared to other standardized
distributions
· A RAW score by itself does not provide much information about it's position within a
distribution
· Z-scores tell us exactly where your score is located in relation to EVERYBODY else
Two parts to a z-score
· The z-score transforms each X value into a signed value (+ or -)
· Note the z-score has two parts that are absolutely necessary - the SIGN and the VALUE
formula: z = (X - mean)/(standard deviation)
- numerator is a deviation score
- Denominator expresses deviation in standard deviation units
determining a raw score from a z-score - ANS ✔✔formula: X = m + z(standard deviation)
,using z-scores to standardize a distribution (purpose #2) - ANS ✔✔It is possible to transform
every X value in a distribution to z-scores - called a standardized distribution
standardized distribution - ANS ✔✔a distribution of scores that have been transformed to
create predetermined values for m (mean) and s (standard deviation) .
features of a standardized distribution - ANS ✔✔a) Shape - the shape of a standardized
distribution DOES NOT change from it's original shape
b) The Mean - standardized distributions ALWAYS have a mean of zero
c) Standard Deviation - standardized distributions always has an SD of 1
using z-scores for making comparisons - ANS ✔✔you cannot compare two exam scores from
different courses and really know anything about which course you're doing better in.
however, you can standardize both sets of distributions in order to make a comparison.
other standardized distributions based on z-scores - ANS ✔✔1. Using a Predetermined μ and σ
· Some distributions are famous for having predetermined values of μ and σ - such distributions
are computed to avoid negative values and decimals in the z-score
· Examples - IQ test and achievement test distributions
2. Two step process for transforming a distribution to predetermined values
a) Raw scores are transformed into z-scores
b) Z-scores are transformed into new X values so the specific mean and SD are attained
, probability - ANS ✔✔when several outcomes are possible, probability is the likelihood of any
particular outcome expressed in terms of a fraction or proportion.
formula: Probability of A = number of outcomes classified as A / total number of possible
outcomes
probability notation - ANS ✔✔notation: p(example) = the probability of the specific outcome
· Note - probability is defined as a proportion (fraction) - any probability question can be
restated as a proportion problem
· Note - probabilities range from 0 to 100
random sampling - ANS ✔✔requires the satisfaction of two requirements:
a) Each individual in the population must have an equal chance of being selected
- The "equal chance" requirement applies to individuals. Individual probabilities are combined
to find probabilities for groups.
b) If more than one individual is selected, there must be constant probability for each and every
selection
· Without replacing the selected sample - the rule of constant probability is violated
· Probability predicts samples not populations
probability and frequency distributions - ANS ✔✔Probability usually involves scores that can be
displayed in a frequency distribution graph
probability and the normal distribution - ANS ✔✔· Some things about the normal distribution
- It is symmetrical - what does this mean with respect to proportions?
