Respuesta :
Answer:
A. .1070
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they make a purchase, or they do not. The probability of a customer making a purchase is independent from other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Forty-four percent of customers who visit a department store make a purchase.
This means that [tex]p = 0.44[/tex]
What is the probability that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase?
This is [tex]P(X = 6)[/tex] when n = 9. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{9,6}.(0.44)^{6}.(0.56)^{3} = 0.1070[/tex]
So the correct answer is:
A. .1070
Answer: A. .1070
Step-by-step explanation:
We would apply the formula for binomial distribution which 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 customers sampled.
From the information given,
p = 44% = 44/100 = 0.44
q = 1 - p = 1 - 0.44
q = 0.56
n = 9
x = r = 6
Therefore,
P(x = 6) = 9C6 × 0.44^6 × 0.56^(9 - 6)
P(x = 6) = 84 × 0.0073 × 0.175616
P(x = 6) = 0.107
