Statistics: Mean and Standard Deviation Quiz

The average number of successes in a fixed number of independent trials, where each trial has the same probability of success.

Measures the spread or variability of the distribution of successes.

The square root of the variance, providing a measure of the typical distance of observed values from the mean.

The average outcome of an experiment after a large number of repetitions.

A rough estimate of the range of usual values for a probability distribution.

The lowest value considered likely to occur in a data set.

The highest value considered likely to occur in a data set.

Number of trials in a binomial experiment

Probability of success in a single trial

Probability of failure in a single trial. q = 1 - p

The expected value of the number of successes in a binomial experiment, calculated as n * p, where n is the number of trials and p is the probability of success in each trial.

The measure of the spread of the number of successes in a binomial experiment, calculated as the square root of n * p * (1 - p).

A result that falls outside the typical range of outcomes, considered unlikely if the assumed probability is accurate.

The interval containing most of the expected values in a distribution, usually within plus or minus two standard deviations from the mean.

A probability distribution that describes the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success.

The count of favorable outcomes (successes) within a specific number of trials or within a sample group.

The total number of observations or items in a sample.

The likelihood of a specific outcome (success) in a single trial.

A probability distribution that is symmetrical and bell-shaped. Many natural phenomena follow this pattern.

A stated probability or percentage (16%) of an event occurring

A discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space, if these events occur with a known average rate and independently of the time since the last event.

The random variable must count occurrences of an event over a specific interval. Occurrences must be random, independent, and uniformly distributed over the interval.

Events that don't happen very often, but can still be predicted probabilistically with Poisson

A mathematical formula used to calculate the probability of a given number of events occurring within a fixed interval. It involves the average rate of events (λ) and the factorial function.

The specific period of time, area, or space in which the occurrence of events is being measured.

The number of customers arriving at a store in an hour, the number of misprints in a book, counts of radio-active decays.

A probability distribution that models the probability of a given number of events occurring in a fixed interval of time or space, if these events occur with a known average rate and independently of the time since the last event.

A probability distribution that describes the probability of getting a specific number of successes in a fixed number of independent trials, where each trial has the same probability of success.

Using the Poisson distribution to estimate probabilities from a binomial distribution when the number of trials (n) is large and the probability of success (p) is small.

Conditions for using the Poisson distribution as an approximation to the binomial: n ≥ 100 and np ≤ 10, where n is the number of trials and p is the probability of success.

The mean of the Poisson distribution, often calculated as np (product of number of trials and probability of success).

Specifies the chance of a particular number of events (x) occurring within a given interval, calculated using the Poisson distribution formula.

A probability distribution that models the number of events occurring in a fixed interval of time or space, where these events occur independently and at a constant average rate.

The average number of events expected in the specified interval.

The actual count of events in a given interval.

A Poisson distribution is appropriate when modeling events that occur independently and at a constant average rate, within a specified interval of time or space.

Number of heart attacks in a specific region over a year, assuming independence between individuals.

Number of plane landings at an airport in a specific time interval, but likely not independent due to scheduling and traffic.

Number of car punctures on a highway over a year, although there could be factors leading to non-independence.

Number of homes flooded in a region in a specific time period, likely not independent because floods affect multiple homes.

Calculating the likelihood of a specific number of events occurring in a given time frame, given the average rate.