Afriend tells you that she has conducted a survey to find the proportion of people in her university that utilize the campus internet cafe at least once a day. she has collected a sample and calculated a sample proportion of p^ = 0.31. she uses this value to calculate a confidence interval for the population proportion. your friend says that she is not going to tell you the sample size or the level of confidence used in her construction, and wants you to guess what the confidence interval is. she gives you 5 options.
select the interval(s) that, based on the information given, could possibly be the confidence interval your friend calculated:
a. the interval between 0.68 and 0.88
b. the interval between 0.58 and 0.78
c. the interval between 0.48 and 0.78
d. the interval between 0.58 and 0.88
e. the interval between 0.48 and 0.68

step-by-step explanation:

where is the question is there is a formula or is there not one

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.