A time study of a factory worker has revealed an average observed time of 3.20 ?minutes, with a standard deviation of 1.00 minute. 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.)

a) 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? =______ observations? (round your response up to the next whole? number)

b) Based on the? findings, the conclusion would be that the current sample size of 45 is (adequate or not adequate) for the time study.