Using the R functions pbinom $(),$ pnorm $(),$ and ppois $(),$ determine which of the following options are correct for $n=1000$ and $p=0\mathrm{.}01.$ Note that More than one option may be correct.

Using the Poisson approximation, $P(x>20)$ is $0\mathrm{.}001588($rounded to $6$ digits$)$

Using the Poisson approximation, $P(x<mn>1</mn><mn>5</mn><mi>)</mi>$ is $0\mathrm{.}951260($rounded to $6$ digits$)$

Using the Normal approximation, $P(x20)$ is $0\mathrm{.}999259($rounded to $6$ digits$)$

$P(x10)$ is better approximated by the Poisson distribution than the Normal distribution.

Using the Normal approximation, $P(x<mn>2</mn><mn>0</mn><mi>)</mi>$ is $0\mathrm{.}998504($rounded to $6$ digits$)$