Confidence Interval (one sample)

A simple random sample of 50 items resulted in a sample mean of 32 and a sample standard deviation of 6. Obtain 95% confidence interval for the population mean.

This is the question. I am using t-test and getting the C.I. as (31.3037, 32.6963). I did linear interpolation to get the value of t49, because only values of t40 and t50 are given in t-table. But, it did not match with the given answer i.e. (30.295, 33.705). How did they get the interval (30.295, 33.705) can anyone kindly help me to understand please?

My another query is how are you people recognizing whether the sum requires 1-sample discrete or 1-sample continuous test statistic formula? Like, in this question, nothing is specifically mentioned.

 

The answer is matching using t-test, you may have made a mistake.
But here, the sample is large i.e. n>30 then I guess Z approximation would be appropriate. Using Z approx., the CI is (30.337,33.663). See, whether its a correct answer or not. Have they used t-test in the solution?

 

Thank you Bharti. I'm so sorry, just did a silly mistake in calculation.