Forty-four percent of customers who visit a department store make a purchase. What is the probability that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase?

A. .1070

B. .1752

C. .8930

D. .0033

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.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

Forty-four percent of customers who visit a department store make a purchase.

This means that

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 when n = 9. So

So the correct answer is:

A. .1070

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

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116