Forty-four percent of customers who visit a department store make a purchase. The probability, rounded to four decimal places, that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase is:

(.44)^6 * (1-.44)^3 = ?

.0013

To calculate the probability, we need to use the binomial probability formula. The formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:
P(X = k) is the probability of getting exactly k successes
C(n, k) is the number of combinations of n items taken k at a time
p is the probability of success
n is the number of trials

In this case, the probability of a customer making a purchase is 44% or 0.44, and the number of trials is 9. We want to calculate the probability of exactly 6 customers making a purchase.

Using the formula, we can substitute the values:

P(X = 6) = C(9, 6) * 0.44^6 * (1 - 0.44)^(9 - 6)

To calculate C(9, 6), we use the formula:

C(n, k) = n! / (k! * (n - k)!)

C(9, 6) = 9! / (6! * (9 - 6)!) = 9! / (6! * 3!)

Now, we can calculate each part of the formula:

C(9, 6) = (9 * 8 * 7 * 6!) / (6! * 3 * 2 * 1) = (9 * 8 * 7) / (3 * 2 * 1) = 84

P(X = 6) = 84 * 0.44^6 * (1 - 0.44)^3

Calculating the values:

P(X = 6) = 0.0221 (rounded to four decimal places)

Therefore, the probability that exactly 6 out of 9 customers will make a purchase is approximately 0.0221.