A methods and measurements analyst for Digital Devices needs to develop a time standard for the task of assembling a computer mouse In a preliminary study, she observed one of her workers perform this task six times with the following results: $56$ Observation Time $($seconds $238340434464240$ How many observations should be made if she wants to be $86\mathrm{.}64$ percent confident that the maximum error in the observed time is $\mathrm{.}5$ second? Assume that the standard deviation of the task time is four seconds.