Probability of Exact Expenditure: A Normal Distribution Approach with Continuity Correction

A statistical analysis using normal distribution and continuity correction to model probability of exact expenditure.

Hunter Harris

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Probability of Exact Expenditure: A Normal Distribution Approach withContinuity CorrectionIf you are asked to calculate the probability that a randomly selectedemployee’s expenditure is exactly $5, what will be your answer?The probabilitythat a randomly selected employee’s expenditure is exactly $5is0.121Why?I calculated the probability below.It makes sense as the graph has minimum valueat 5.Will your answer be the same for any individual expenditure?No, this answer is just for those who are employees at a certain company with sexactly $5expenditure.What approach would you take to calculating the likelihood of spending exactly$5.00 on a lunch purchase?I used the approach of Normal distribution with approximation to Binomialdistribution as:Meanexpenditure =μ= 7Standard deviation =σ= 2The probability of exactly $5 expenditure =()5P X=Since normal distribution is continuous so we have to take continuity correctionas:

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