The Owner of Kat Motel Wants to Develop a Time

Multiple Choice

The owner of Kat Motel wants to develop a time standard for the task of cleaning a cat cage. In a preliminary study, she observed one of her workers perform this task six times, with the following results: $$\begin{array} { | l | c | c | c | c | c | c | } \hline \text { Observation } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Time(Seconds) } & 99 & 87 & 90 & 81 & 93 & 90 \\\hline\end{array}$$ How many observations should be made if she wants to be 95.44 percent confident that the maximum error in the observed time is two seconds? Assume that the standard deviation of the task time is six seconds.

A)  5
B)  6
C)  30
D)  36
E)  49