Question: Suppose you were performing a telephone survey & contacting 8 people. The probability of reaching a person is 40%
B. Based on A, how many people would you be most likely to reach?





C. If you repeated this experiment 1000 times, how many times would you expect to get all 8 people on the phone?




D. If you repeated this experiment 1000 times, how many times would you expect to reach none?





E. What is the mean value for this distribution?






F. What is the variance?




A. Construct a probability distribution for all possible outcomes (hint: Binomial formula)

  Edit

Answer: 1. A: Probability distribution:
Let x is a random variable denotes the no. of people reached.
so, x takes values 0,1,2...,8.
Using binomial distribution need to find all P(x=0), P(x=1),.....P(x=8) values.
Here prob. of sucess=40%=0.4 so, q=1-p=0.6
P(x=0)=8c0*(0.4)^0*(0.6)^8=0.0167
P(x=0)=8c1*(0.4)^1*(0.6)^7=0.09
P(x=0)=8c2*(0.4)^2*(0.6)^6=0.209
P(x=0)=8c3*(0.4)^3*(0.6)^5=0.279
P(x=0)=8c4*(0.4)^4*(0.6)^4=0.232
P(x=0)=8c5*(0.4)^5*(0.6)^3=0.124
P(x=0)=8c6*(0.4)^6*(0.6)^2=0.041
P(x=0)=8c7*(0.4)^7*(0.6)^1=0.008
P(x=8)=8c8*(0.4)^8*(0.6)^0=0.001

The required distribution is:
x: 0 1 2 3 4 5
6 7 8
P(x): 0.0167 0.09 0.209 0.279 0.232 0.124 0.041
0.008 0.001  Edit