Answer: a) 0.113
b) 0.859
c) 0.141
Step-by-step explanation:
We would assume a binomial distribution for the number of consumers who prefer to purchase groceries online.. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 20% = 20/100 = 0.2
q = 1 - p = 1 - 0.2
q = 0.8
n = 16
a) P(x = 1)
P(x = 1) = 16C1 × 0.2^1 × 0.8^(16 - 1)
P(x = 1) = 0.113
b) P(x > ) = 1 - P(x ≤ 1)
P(x ≤ 1) = P(x = 0) + P(x = 1)
P(x = 0) = 16C0 × 0.2^0 × 0.8^(16 - 0
P(x = 0) = 0.028
P(x = 1) = 0.113
P(x > ) = 1 - (0.028 + 0.113) = 0.859
c) P(≤ 1) = P(x = 0) + P(x = 1)
P(≤ 1) = 0.028 + 0.113 = 0.141
