When an opinion poll selects cell phone numbers at random to dial, the cell phone exchange is first selected and then random digits are added to form a complete telephone number. When using this procedure to generate random cell phone numbers, approximately 55%55% of the cell numbers generated correspond to working numbers. You watch a pollster dial 1515cell numbers that have been selected in this manner.
What is the mean number of calls that reach a working cell number?
a. 0.550.55b. 1515c. 8.258.25d. 3030

c. 8.25

Step-by-step explanation:

The given scenario corresponds to binomial experiment because

1. There are two possible outcomes i.e. each number can be working or not working.

2. On each dialing the probability of getting working cell number is p=0.55.

3. Cell phone numbers are randomly dialed so these are independent.

4. A pollster dialed 15 cell numbers i.e. n=15.

The mean number of calls that reach a working cell number can be calculated by computing mean of binomial distribution using the given information.

Mean of binomial distribution=E(x)=np

The mean number of calls that reach a working cell number=15*0.55=8.25

Thus, the mean number of calls that reach a working cell number=8.25