Among homeowners in a metropolitan area, 25% recycle paper

Solution :

Step 1 of 3:

Let X denotes the number of customers who recycle paper in a week.

Let p denotes the probability that the recycle paper in a week is 0.25 and

Let  n denotes the total number of house owners is 10000.

Here we can use normal approximation.

Z =

Where,

np = 10000(0.25) = 2500  and

n(1-p) = 10000(1-0.25)

n(1-p) = 10000 (0.75)

n(1-p) = 7500

Our goal is:

a). We need to find the probability that the more than 2600 recycle paper in a week.

b). We need to find the probability that the between 2400 and 2600 recycle paper in a week .

d). We need to find the number of customers who recycle paper in a week.

a). The probability that the more than 2600 recycle paper in a week is

P(X>2600) = P

P(X>2600) = P

P(X>2600) = P

P(X>2600) = 1-

Using areas under the normal curve table,

P(X>2600) = 1-0.9899

P(X>2600) = 0.0101

Therefore, the probability that the more than 2600 recycle paper in a week is 0.0101.