Audio cassette tapes of a particular brand are claimed by the manufacturer to give, on average, at least 60 minutes of playing time. After receiving some complaints, the manufacturer’s quality control...

Audio cassette tapes of a particular brand are claimed by the manufacturer to give, on average, at least 60 minutes of playing time. After receiving some complaints, the manufacturer’s quality control manager obtains a random sample of 64 tapes and measures the playing time, t minutes, of each. The results are summarized by
∑t=3953.28 and ∑t²=244,557.00

Construct a symmetric 99% confidence interval for the population mean playing time of the brand of tape.
Does the confidence interval support the customer’s complaints? Give a reason for your answer.