Question

The duration of the AstraZeneca Covid-19 vaccine side effect is normally distributed with a mean of 1.5 days and a standard deviation of 0.4 days.

(i) If a AstraZeneca Covid-19 vaccine recipient is selected at random, find the percentage

that the duration of side effect is less than 24 hours. (3 marks)

(ii) 96% of the AstraZeneca Covid-19 vaccine recipients have experienced more than k days of discomfort symptoms. Find the value of k. (3 marks)

(iii) 7 AstraZeneca Covid-19 vaccine recipients are selected randomly, find the probability

that 3 recipients have less than 24 hours of side effect.

Answer 1

i)

$z=\frac{x-\mu}{\sigma}=\frac{1-1.5}{0.4}=-1.25$

$P(x<1)=P(z<-1.25)=0.10565$

ii)

$P(x>k)=0.96$

$P(x<k)=1-0.96=0.04$

z for 0.04:

$z=\frac{k-\mu}{\sigma}=\frac{k-1.5}{0.4}=-1.25$

$k=1.5-1.25\cdot 0.4=1$ day

iii)

Binomial distribution

$p=P(x<1)=0.10565$ (from part i))

$n=7$

$P(k=3)=C^3_7p^3q^4=\frac{7!}{3!4!}\cdot0.10565^3\cdot(1-0.10565)^4=0.0264$