7.4-5. A quality engineer wanted to be $98 \%$ confident that the maximum error of the estimate of the mean strength, $\mu$, of the left hinge on a vanity cover molded by a machine is 0.25 . A preliminary sample of size $n=32$ parts yielded a sample mean of $\bar{x}=35.68$ and a standard deviation of $s=1.723$.
(a) How large a sample is required?
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