The time in hours that a technician requires to perform preventative maintenance

Question

The time in hours that a technician requires to perform preventative maintenance on an air conditioning unit has a mean time of 1 hour and a standard deviatioion also of 1 hour. your company has a contract to maintain 70 of these units in an apartment building. you must schedule technicians time for a visit to this building. consider the 70 air conditioners as a SRS from all units of this type. a. what is the sampling distribution for the mean time spent working on these units. How do you know this? b. What is the probability that the average maintenance time spent for these 70 units exceeds 1.1 hours? c. what is the probability that the average maintenance time spent for these 70 units exceeds 1.25 hours? d. is it safe to budget an average of 1.1 hours for each unit? or should you budget an average of 1.25 hours? why?

Explanation / Answer

Ans:

Mean=1 hr

standard deviation =1 hr

a)Central limit theorm is applicable here,as n=70>30.

Sampling distribution of sample follow normal distribution:

mean=1 hr

std dev=1/sqrt(70)=0.12

b)

z=(1.1-1)/0.12=0.833

P(z>0.833)=0.2024

c)

z=(1.25-1)/0.12=2.083

P(z>2.083)=0.0186

d)It is safe to budget an average of 1.25 hrs,as probability of average maintenance tme exceeds 1.25 hrs is very low.

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