Based on historical data in Oxnard college, we believe that $27\%$ of freshmen do not visit their counselors regularly. A random sample of $73$ freshmen will be used to estimate the proportion of the students who do not visit their counselors regularly. Show your answer to $4$ decimal places if necessary.

a$.$ What is the distribution of widehat$(p)?$widehat$(p)N_1$

b$.$ What is the probability that the sample proportion more than is $0\mathrm{.}31?$

c$.$ What is the probability that the sample proportion is between $0\mathrm{.}26$ and $0\mathrm{.}32?$