Even though the chances of developing a blood clot or low platelets after receiving the AstraZeneca vaccine is very low, many people in Japan, say 45% of individuals aged over 50 years, feel uncomfortable taking the AstraZeneca COVID-19 vaccine. Suppose a random sample of 300 adults aged over 50 years from a regional town in Southern Japan was selected and asked their preference of taking the AstraZeneca COVID-19 vaccine or not. Find the probability that at least 50% of the regional town residents in the sample do not prefer the AstraZeneca vaccine, using

a) the exact binomial distribution, and

b) the approximate sampling distribution

c) Do you think the approximation in b) is accurate? Explain your answer by showing that the conditions required are either met or not met