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**

based on a survey, assume that 53% of consumers are comfortable
having drones deliver their purchases. suppose we want to find the
probability that when 4 condumers ate randomly selected, exactly 2
of them are comfortable with the drones. what is wrong eith using
the multiplication tule to find the probability of getting 2
vonsumers comfortable with drones followed by 2 consumers not
comfortable, as in calculation:
(0.53)(0.53)(0.47)(0.47)=0.0621?

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