A time study of a factory worker has revealed an average observed time of 3.20 ​minutes, with a standard deviation of 1.28 minutes. These figures were based on a sample of 45 observations. Assume that the firm wants to be 99​% confident that the standard time is within 5​% of the true value. ​(Round all intermediate calculations to two decimal places before proceeding with further​ calculations.) Based on the given information and the given confidence level and accuracy​ level, the number of observations that would be necessary for the time study​