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% of the cell numbers generated correspond to working numbers. You watch a pollster dial 15 cell numbers that have been selected in this manner.
(a) What is the mean number of calls that reach a working cell number?
0.55
15
8.25
30
(b) What is the standard deviation ????σ of the count of calls that reach a working cell number?
0.55
2.872
1.927
3.7125
(c) Suppose that the probability of reaching a working cell number was p=0.70p=0.70 . How does this new pp affect the standard deviation?
When p=0.70,σ=3.24 calls.
When p=0.70,σ=3.15 calls.
When p=0.70,σ=1.775 calls.
When p=0.70,σ=10.5 calls.
What would be the standard deviation if p=0.80 ? (Enter your answer rounded to three decimal places.)
σ=
What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to 1 ?
As p approaches 1 , the standard deviation increases (that is, it approaches 0).
As p approaches 1 , the standard deviation increases (that is, it gets further and further from 0)
As p approaches 1 , the standard deviation remains constant.
As p approaches 1 , the standard deviation decreases (that is, it approaches 0).