Question

# the daily number of visitors to a national park follows a Poisson distribution with mean 900....

the daily number of visitors to a national park follows a Poisson distribution with mean 900.

calculate the 80th percentile of the number of visitors in a day.

We can approximate poisson distribution to normal distribution since mean is large.

Also we need to do the continuity correction since poisson is a discrete and normal is a continuous distribution.

The percentile basically divides the data into 100 parts where each part represent the percent of data that lies below it.

So 80th percentile in form of probability means

P( X < x) = 0.80

The continuity correction

P(X < (x-0.5) ) = 0.80

Converting to normal distribution

P(X < (x-0.5))= 0.80

P(Z < ) = 0.80

We will use normal percentage tables or excel function 'normsinv(p). Note that we have less than type so we will use positive value

= 0.8416

Since no. of people can't be an integer.

So the 80th percentile number of visitors is 926.

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