Provide the correct interpretation of the conﬁdence interval A sample of $150$ new cell phones produced by Yeskia found that $12$ had cosmetic ﬂaws. A $90\%$ conﬁdence interval for the proportion of all new Yeskia phones with cosmetic ﬂaws is $0.044$ to $0.116$. Which ones of statements below provide the correct interpretation of this conﬁdence interval?
  Please, give explanation.
  a) There is a $90\%$ chance that the proportion of new phones that have cosmetic ﬂaws is between $0.044$ and $0.116$. 
  b) There is at least a $4.4\%$ chance that a new phone will have a cosmetic ﬂaw. 
  c) A sample of $150$ phones will have no more than $11.6\%$ with cosmetic ﬂaws. 
  d) If you selected a very large number of samples and constructed a conﬁdence interval for each, $90\%$ of these intervals would include the proportion of all new phones with cosmetic ﬂaws. 
  e) none of the above


I would say that the answer is a) based on my poor understanding of definition of CIs.
The answer should be (d).

(d) should be the standard correct choice. The probability that the confidence interval you constructed would include the actual number would be 90%. But strangely enough, this choice doesn't actually invoke any numbers in the question.

(a) can sound correct or wrong depending on interpretation, so not a good choice just to be safe. It's not true that conditioned on these number computed for confidence interval, the actual number lie inside it at probability 90%.

(b) too absolute to be true. There is still the possibility that the actual number is lower than estimated.

(c) same problem as (b)

(e) is out since (d) is quite correct.
The answer should be (d).

(d) should be the standard correct choice. The probability that the confidence interval you constructed would include the actual number would be 90%. But strangely enough, this choice doesn't actually invoke any numbers in the question.

(a) can sound correct or wrong depending on interpretation, so not a good choice just to be safe. It's not true that conditioned on these number computed for confidence interval, the actual number lie inside it at probability 90%.

(b) too absolute to be true. There is still the possibility that the actual number is lower than estimated.

(c) same problem as (b)

(e) is out since (d) is quite correct.