Question

Ontario has decided to allow outdoor activities amid COVID 19 with some restrictions. Dr. David Williams, Chief Medical Officer of health, is recommending that people wear face masks and maintain physical distancing in public places. You have estimated that 80% of people outdoors would be wearing a face mask. To decide for yourself, you have conducted a survey on June 28^th in one of the “Active” outdoor zones in Toronto.

(a) On June 28^th you have sampled 25 people that were outdoor to see if they are wearing face masks.

i) Calculate the probability that more than 15 outdoor people were wearing face masks.

ii) Calculate the probability that at least 10 but no more than 14 outdoor people were wearing face masks.

(b) On another day you have sampled 80 people that were outdoor who are wearing face masks.

i) Find the expected number of people that are outdoor who are wearing face masks.

ii) Find the variance of the people that are outdoor who are wearing face masks.

(c) Using the solution you found in part b), determine the following:

i) E(4X+2)

ii) V(2X+3)

(d) On another day, you decided to sample 6 people that were outdoor, and you think that 77% will be wearing a facemask. What is the probability that 4 outdoor people will be wearing a facemask?

Answer 1

a)

i)

ii)

b)

i)

Expected number E(X) = n*p = 80*0.8=64

ii)

variance = n*p*(1-p)=12.8

c)

i)

E(4X+2) = 4E(X)+2 = 258

ii)

V(2X+3) = 2² V(X) + V(3) = 4*12.8+0=51.2

d)