A randomised, single-blind, phase 1/2, controlled trial of ChAdOx1 nCoV-19 vaccine was done in healthy adults in the UK, and described in a recent publication (July 20th 2020, The Lancet). In a preliminary report, the authors describe the immunogenicity, reactogenicity, and safety of vaccination with 5??10¹⁰ viral particles of ChAdOx1 nCoV-19 showing an acceptable safety profile, and increased antibody responses.

After the vaccination procedure, participants were asked to record any adverse events using electronic diaries during the 28-day follow-up period.

Local and systemic reactions were more common in the ChAdOx1 nCoV-19 group than in the control group and many were reduced by the use of prophylactic paracetamol, including pain, feeling feverish, chills, muscle ache, headache, and malaise (all p

In the following questions,we focus only on the group of people who received the vaccine but did not get paracetamol.In that group,the number of participants who felt headaches after the vaccinewithout paracetamol is 331 participants out of the 487. The authors report a 95% confidence interval for the proportion of people who felt headaches after the vaccinewithout paracetamol to be 64%-72%.

a)Let X be the number of people out ofn randomly selected people reporting headaches after the vaccine without paracetamol, and letpbe the true proportion of people feeling headaches after the vaccine without paracetamol.

Under the usual assumptions, what is the true distribution of X?

won1) 03(n,%) 01301,?) OMM) Under the usual assumptions, what is the approximate distribution of X? (mm7;) ON( ,\\/P(1,;P)) 01ml)