(Binomial distribution) Forty-four percent of customers who visit a department store make a purchase. The probability that in a random sample of 10 customers who will visit this department store, exactly six will make a purchase is.

The probability that exactly six will make a purchase is 0.15

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 trials or sample.

From the information given,

p = 44% = 44/100 = 0.44

q = 1 - p = 1 - 0.44

q = 0.56

n = 10

x = r = 6

Therefore,

P(x = 6) = 10C6 × 0.44^6 × 0.56^(10 - 6)

P(x = 6) = 210 × 0.0073 × 0.098

P(x = 6) = 0.15

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: