Use the Poisson distribution to find the indicated...

Name: Problem 9, Chapter 5: Elementary Statistics
Uploaded: 2021-05-07T16:48:02-08:00
Duration: 1 min 34 s
Channel: Sheryl Ezze
Description: Use the Poisson distribution to find the indicated probabilities. In a recent year, NYU-Langone Medical Center had 4221 birhs. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births?

Use the Poisson distribution to find the indicated probabilities. In a recent year, NYU-Langone Medical Center had 4221 birhs. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births?

Use the Poisson distribution to find the indicated probabilities.
In a recent year, NYU-Langone Medical Center had 4221 birhs. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births?

Key Concepts

Interpretation of Results

Interpreting the outcome of a probability calculation involves comparing the calculated probability to typical thresholds for common or rare events. A very small probability value indicates that the specific number of events (such as an exact count) is unlikely, even if the event itself is possible under the overall distribution model.

Probability Mass Function

The probability mass function (PMF) of the Poisson distribution gives the probability of observing exactly k events in the interval and is defined as P(X=k) = (?^k * e^(-?))/k!, where ? is the mean rate of events. This function is used to calculate the likelihood of different outcomes given the average event rate.

Poisson Distribution

The Poisson distribution is a probability distribution that models the number of events occurring in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event. It is especially useful for counting rare events or events that occur randomly over time or area.

Mean Rate Calculation

The mean rate in the context of the Poisson distribution represents the expected number of events in the chosen interval. It is calculated by dividing the total number of events by the number of intervals, which provides the average rate that serves as a key parameter for the distribution.

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