Answer:
Mean = 20
Variance = 16
Step-by-step explanation:
Solution:-
- Let X be the number of customers paying with a debit card. X has the binomial distribution with n = 100 trials and success probability p = 0.2
- In general, if X has the binomial distribution with (n) trials and a success probability of (p) then:
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.
- The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
- Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.
X ~ Binomial( n = 100 , p = 0.2 )
- The mean of the binomial distribution is n * p = 20
- The variance of the binomial distribution is n * p * (1 - p) = 16
