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? B I U A - A - I E = = x x, = E 12pt Paragraph fr

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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?
B I U
A
I E E E
x x, E E
12pt
Paragraph
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? B I U A I E E E x x, E E 12pt Paragraph
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