To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail. (a) What percent of values must be chopped off from each tail for a 95% confidence interval?
(b) If the bootstrap distribution contains values for 1000 bootstrap samples, how many should be chopped off at each end to produce a 95% confidence interval?

a

b

Step-by-step explanation:

From the question we are told that

   The number of bootstrap samples is  n =  1000

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally the percentage of values that must be chopped off from each tail  for a 95% confidence interval is mathematically evaluated as

=>    

Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is

=>  

=>  

it would be 6xy and -16xy.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.