Students at a certain school were surveyed, and it was estimated that 20% of college students abstain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it to within 0.08 with probability 0.95, if before conducting the study (a) you are unwilling to predict the proportion value at your school and (b) you use the results from the surveyed school as a guideline.

a) A sample size of at least 251 students is needed.

b) A sample of at least 97 students is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

(a) you are unwilling to predict the proportion value at your school

We need a sample size of at least n.

n is found when M = 0.08.

We wont predict a proportion value for the school, so we use

So

Rounding up

A sample size of at least 251 is needed.

(b) you use the results from the surveyed school as a guideline.

Now we have that

So

Rounding up

A sample of at least 97 students is needed.

square root

step-by-step explanation:

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1