Answer:
<em>A) It fulfills the condition of binomial experiment</em>
<em>B) P (x=12) =0.1678</em>
<em>C)P ( x ≥16)= 0.1011</em>
<em>d) P (x>17) =0.0096 < 0.5</em>
Step-by-step explanation:
A. The binomial probability distribution has the following four properties
1. the outcomes of each trial maybe classified into success and failure.
2) the probability of success p remains constant for all trials.
3) the successive trials are all independent.
4) the experiment is repeated a fixed number of times ,n.
<em>These all conditions are fulfilled by the given question so it is a binomial experiment. </em>
<em></em>
B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678
C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)
where
P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645
P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270
P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080
P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015
P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001
so
P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011
d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)
=0.0270 +0.0080+ 0.0015+0.0001
=0.0096
From this we see that the probability of more than 17 people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.
