Based upon past experience, 1% of the telephone bills mailed to households are incorrect. A sample of 20 bills is selected.
p= probability of success= 0.01 n= number of trails= 20 q= probability of failure = 0.99
a. What is the probability that 10 of the bills is incorrect?
b. What is the probability that at least one bill is incorrect?
c. What is the probability that more than 15 of the bills is incorrect?
d. How will answers change if more than 20 bills is selected?
e. Based on your answers, what is your conclusion?
f. If this is a Binomial experiment, what are the 2 mutually exclusive outcomes?
g. What is/are your assumptions to calculate the above answers?
Answer: in this problem, let X be number of the incorrect telephone bills. Then X has a binomial distribution with n=20 and p=0.01.
Hence, the formula for binomial is P(X=x)=C(20,x)*0.01^x*0.99^(20-x).
a. P(10 is ...
The soluton discusses the assumption and property and calculates the probability for binomial random variable.