Find the probability that Mr. Thomas's estimates of average sales growth and percentage of employee having MBA fall within 2% of management's perception in both cases for east and south zones?

Mr. Thomas joined First Buy, an FMCG company, in April 2021. Thomas reported to Ms. Bishop. At the end of October 2020, the senior management team of First Buy got the information from the regional heads that, on average, the sales had gone up by 20% in Eastern and Southern regions, whereas the North and West regions had shown a flat sales growth of 10% in the second quarter (July-Sep'20). Although the team had not seen the actual sales figures or any such analysis, the estimates suggested that it was not different from the trend observed in past four quarters, unless verified. In fact, one of the regional heads quoted that the variation in the sales growth as captured by standard deviation, over the past few years in all four regions is about 4%. The management knew that this growth was not driven by the marketing and advertising expenses as the budget is almost equally allocated to each region. They thought that improvement in sales growth in the East and South regions might be driven by the change in employee composition. There had been some new recruitment having background of MBA in marketing & sales in these two regions in the past one year. In fact, the perception was that 60% of the sales executives have MBA background.

Thomas to work with four and half years (Apr'17-Aug'21) of sales data (approx.) for all the four regions (North, East, South and West). Thomas knew the data source, but he also knew that collecting four and half years of data would take more than half a day. This made Mr. Thomas wondered how he should proceed to extract the data and analyze the results without missing the deadline. By the end of the day, Thomas derived that the average sales growth for the data span is 30% for 54 observations (i.e. four and half years of monthly sales figures) and the percentage of sales executives having MBA background is around 55% in the Eastern and Southern regions. He also noted that out of total 2000 sales employees, only 400 were employed in the East and South zones.