Statistical Analysis of Work-Hours Distribution and Probability CalculationsOverall, the amount of work-hours involved in the festival preparation by companyemployees is normally distributed around 150 hours with a standard deviation of20 hours.1)How likely (what is the probability) is it that somebody will have hisinvolved work-hours between 140 and 170?Solution.Let X be theamount of work-hours involved in the festival preparationby company employees. Then we know that X follows a normal distribution with.20,150==So,the probabilitythat somebody will have hisinvolved work-hours between 140 and 170is)170140(XPNote that)1,0(~20150NZX−=. So,)170140(XP)5.0()1()15.0()(201501702015020150140−−=−==−−−ZPZPZPPXBy looking up the z-table, we have3085.0)5.0(8413.0)1(=−=ZPZPSo,)170140(XP5328.03085.08413.0)5.0()1(=−=−−=ZPZPPreview Mode
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