The shop foreman has estimated that the proportion of time the machines in her department are idle is a mere 10%. on the basis of this estimate, a work sampling study is to be performed. (a) if we want a 95% confidence level that the true value of the proportion idle time is within ±2.5% of this 10% (that is, the confidence interval runs from 7.5% to 12.5%), how many observations must be taken? (b) suppose after the study is taken with the number of observations from part (a) the proportion of observations is actually 15% rather than 10%. what is the range of the 95% confidence interval in this case? (c) how many more observations need to be taken to achieve a confidence interval of 15% ±2.5%?