Problem $5(15$ points$)$

A communication system protocol transmits data packets over a wireless network. Each de packet has a certain probability of being received with errors. The data error rate of the system is $20\%.$ A communication engineer is working on a project to improve the reliability of the communication system. The engineer claims that the new developed protocol is more reliable than the current protocol. To test this claim, $100$ data packets are sent using the new protocol and the number of unsuccessfully received packets is calculated. If less than $18$ bits are unsuccessfully received, the claim is accepted.

a$.$ What is the probability of committing type $1$ error?

b$.$ What is the probability of committing type $11$ error if the data error rate of the new protocol $\mathrm{.}9\%2$

c$.$ How can you decrease type $1$ error without changing the sample size? How will this affect type II error?