Question

Your company has a contract to perform preventive maintenance on thousands of air-conditioners in a large city. Based on service records from previous years, the time that a technician spends servicing a unit averages one hour with a standard deviation of one hour. In the coming week, your company will service a simple random sample of 60 units in the city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time? (Suppose your company will assume this is enough time if there is a 90% chance the maintenance will be less than 1.1 hours. Round your answer to four decimal places.) The probability it will take less than 1.1 hours is approximately___. Because this is less than or greater than 90%, more time is or is not needed?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	1
std deviation   =σ=	1.000
sample size       =n=	60
std error=σx̅=σ/√n=	0.12910

probability =P(X<1.1)=(Z<(1.1-1)/0.129)=P(Z<0.77)=0.7794

Because this is less than 90%, more time is needed