A survey of 250 students is selected randomly on a largeuniversity campus. They are asked if they use a laptop in class totake notes. The result of the survey is that 115 of the 250students responded​ \"yes.\" An approximate 95​% confidence intervalis (0.397​,0.523​). Which of the following are​ true? If they arenot​ true, briefly explain why not

a)95​% of the students fall in the interval​(0.397​,0.523​).

​b) The true proportion of students who use laptops to takenotes is captured in the interval left parenthesis 0.397 comma0.523 right parenthesis with probability 0.95.

​c) There is a 46​% chance that a student uses a laptop to takenotes.

​d) There is a 95​% chance that the student uses a laptop totake notes 46​% of the time.

​e) We are 95​% confident that the true proportion of studentswho use laptops to take notes is captured in the interval leftparenthesis 0.397 comma 0.523 right parenthesis.

a) Choose the correct answer below.

A. The statement is false. 46​% of the students fall in theinterval ​(0.397​,0.523​).

B. The statement is false. This​ doesn't make sense becausestudents are not proportions.

C. The statement is true.

D. The statement is false. The sample size is too small to makethis claim.

​b) Choose the correct answer below.

A. The statement is false. The population proportion is eitherwithin the interval or not within the interval.

B. The statement is true.

C. The statement is false. The sample size is too small to makethis claim.

D. The statement is false. We are 46​% confident that the sampleproportion of students who use a laptop to take notes is between39.7​% and 52.3​%. ​

c) Choose the correct answer below.

A. The statement is false. There is not enough information tomake an absolute statement about the population value withprecision.

B. The statement is true.

C. The statement is false. There is a​ 5% chance that a randomselected student uses a laptop to take notes.

D. The statement is false. The sample size is too small to makethis claim.

​d) Choose the correct answer below.

A. The statement is false. There is a 54​% chance that a randomselected coworker uses a laptop to take notes.

B. The statement is true.

C. The statement is false. The sample size is too small to makethis claim.

D. The statement is false. This​ doesn't make sense because​it's not about the proportion of the time that a student uses alaptop. ​

e) Choose the correct answer below.

A. The statement is false. We are 46​% confident that between39.7​% and 52.3​% of the samples will have a proportion near95​%.

B. The statement is false. The sample size is too small to makethis claim.

C. The statement is false. The statement should be about thetrue​ proportion, not future samples.

D. The statement is true.