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The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal. (i). Let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of X? (ii). What is the approximate probability that X is less than 2? Show your work and include appropriate graphs of normal density curves of X and Z as illustration. (iii). What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of X.) (iv). Approximately at least how many accidents per week at this intersection will we observe for 95% of the time?

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal. (i). Let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of X? (ii). What is the approximate probability that X is less than 2? Show your work and include appropriate graphs of normal density curves of X and Z as illustration. (iii). What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of X.) (iv). Approximately at least how many accidents per week at this intersection will we observe for 95% of the time?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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"The number of accidents..." please help with i, ii, and iii

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal. (i). Let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of X? (ii). What is the approximate probability that X is less than 2? Show your work and include appropriate graphs of normal density curves of X and Z as illustration. (iii). What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of X.) (iv). Approximately at least how many accidents per week at this intersection will we observe for 95% of the time?
Transcribed Image Text:The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal. (i). Let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of X? (ii). What is the approximate probability that X is less than 2? Show your work and include appropriate graphs of normal density curves of X and Z as illustration. (iii). What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of X.) (iv). Approximately at least how many accidents per week at this intersection will we observe for 95% of the time?
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