Question

With a mean of 16, a Poisson distribution can be approximated by a normal distribution with the same mean. It is known that, under a normal distribution, in between the two lines [mean - 1 standard deviation] and [mean + 1 standard deviation] approximately 68% of the area under the normal curve is covered. If Bigfield is facing its peak demand period with an average of 16 jobs per day and its capacity is set at 20 jobs per day, there is a certain probability P that demand < capacity and all customer orders on any given day can be satisfied by its daily capacity. What is the closest value to P? (Hint: the solving procedure is the same as the last question.) Group of answer choices 95% 84% 68% 97.5%

Answer 1

Mean of the given distribution:

For Poisson distribution, Mean = Variance

This distribution can be approximated as Normal distribution with mean = 16 and SD = 4

We have to find probability that Demand is less than capacity. Here given capacity is 20. Thus we have to find probability that x is less than 20.

i.e. P(x < 20)

Converting x into z score we get,

Converting decimal probability into percentages we get,

P = 0.84 = 0.84*100 = 84%

Hence closest value of P is 84%

(Note that here continuity correction is skipped. If continuity correction is applied then P = 87% and still the closest value remains 84%)