Question

Managers at a local phone service wireless retail center have a goal that 70% of the​ center's customers will have to wait less than five minutes for service. The data below shows the wait times of a random sample of 25 customers in minutes. What is the probability of observing a sample proportion as low or lower than the data presented? Answer to three decimals: 0.123 for example.  

4.1	5.4	2.6	9.8	3.5
3.8	0.4	7.8	4.2	5.8
4.2	2.6	3.5	9.9	6.2
1.5	0.8	9.2	3.2	5.9
2.5	5.3	3.2	2.3	4.5

Answer 1

Number of people who have to wait less than 5 minutes = 16

Proportion of people who have to wait less than 5 minutes, = 16/25 = 0.64

Population proportion, p = 0.70

n= 25

Probability of observing a sample proportion as low or lower than the data presented, P( < 0.64) =

So, the probability of observing a sample proportion as low or lower than the data presented = 0.256

----------------------------------------------------------------------------------------------------

If you have any doubt ask me in comments.