Construct a sequential sampling plan for the cotton fleahopper. Pest control officers need to distinguish fields in which less than $35\%$ of the cotton plants are infested from those in which $50\%$ or more of the plants are infested. They wish to use a$=$B $=0\mathrm{.}10.$

$($a$)$ Calculate the sequential sampling lines and plot them.

$($b$)$ Calculate the expected sample size curve for various levels of infestation.

$($c$)$ Compare you results with those of Pieters and Sterling $(1974).$