Question

Based on a survey, assume that 49% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identity the values of n,x,p and q.

Answer 1

Solution:

Let X denote the number of customers who are comfortable with delivery of their purchases by drones.
here,
-The number of customers (n) is finite.
-The customers are independent of each other.
-The probability of comfort(p) is constant for each customer as, x satisfies the conditions of binomial distribution, so x follows binomial distribution with parameters n and p respectively symbolically X ~ Bin(n,p)
Then,
P[X = x] = nCx p^x q^n-x , p+q = 1
=> P[X = 2] = 4C2 (0.49)^2 (0.51)^4-2, x = 0,1,2...n
=> P[X = 2] = 4!/2!(4-2)! (0.2401) (0.2601)
=>P[X = 2] = 6* 0.06245001 = 0.3747
The values are
n = 4, x = 2, p = 0.49 and q = 0.51