Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
5. Binomial Distribution & Discrete Random Variables
Poisson Distribution
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A student working on a transportation engineering project analyzes traffic flow at an intersection for 20 min. From past data, the average # of cars per minute is 17.6.
(B) Find the probability that the student observes 350 or more cars total.
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B
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1
Step 1: Recognize that the problem involves a Poisson distribution, as it deals with the number of cars arriving at an intersection over a fixed time interval. The average rate (λ) is given as 17.6 cars per minute, and the total observation time is 20 minutes.
Step 2: Calculate the expected total number of cars over 20 minutes. Multiply the average rate per minute (λ = 17.6) by the total time (20 minutes). This gives the mean (μ) of the Poisson distribution for the total number of cars.
Step 3: Since the Poisson distribution can be approximated by a normal distribution for large values of λ, use the normal approximation. The mean (μ) is the expected total number of cars, and the standard deviation (σ) is the square root of the mean: σ = √μ.
Step 4: Standardize the value 350 using the z-score formula: z = (X - μ) / σ, where X is the observed value (350), μ is the mean, and σ is the standard deviation. This converts the problem into finding the probability under the standard normal distribution.
Step 5: Use standard normal distribution tables or software to find the probability corresponding to the z-score. Since the problem asks for the probability of observing 350 or more cars, calculate the area to the right of the z-score (1 - P(Z ≤ z)).
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