Answer: 0.31
Step-by-step explanation:
Let A denotes the event that the students report drinking alcohol and B denotes the students report using some type of tobacco product .
Given : P(A) =0.84 ; P(B)=0.33 and P(A∪B)=0.86
We know that
Then, the probability that the student both drunk alcohol and used tobacco in the past month is given by :-
Hence, the probability that the student both drunk alcohol and used tobacco in the past month = 0.31
Solution:
Required margin of error = 0.05
Estimated population proportion p = 0.8
Significance level = 0.10
The p is 0.8
The significance level, α = 0.1 is , which is obtained by looking into a standard normal probability table.
The number of patients surveyed to estimate the population proportion p within the required margin of error :
= 173.15
Therefore, the number of patients surveyed to satisfy the condition is n ≥ 173.15 and it must be an integer number.
Thus we conclude that the number of patients surveyed so the margin of error of 90% confidence interval is within 0.05 are n= 174.