The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all. Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w21_qp_63 Year：2021 Question No：2
Answer:
\(\mathrm{N}(45.2,45.2)\)
\(\frac{60.5-45.2}{\sqrt{45.2}}[=2.276]\)
\(1-\phi\left({ }^{\prime 2.276}\right)\)
\(0.0114\)
\(\frac{60.5-45.2}{\sqrt{45.2}}[=2.276]\)
\(1-\phi\left({ }^{\prime 2.276}\right)\)
\(0.0114\)
Knowledge points:
6.1.5 use the normal distribution, with continuity correction, as an approximation to the Poisson distribution where appropriate. (The condition that is large should be known; , approximately.)
Solution:
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