An office manager has received a report from a consultant that includes a sectio

Question

An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 48 months and a standard deviation of 6 months. On the basis of this information, determine the proportion of scanners that can be expected to fail in the following time periods:

Use Table A and Table B.

a. Before 40 months of service. (Round z values to 2 decimal places, probability calculations to 4 decimal places and your final answer to 4 decimal places.)

    
b. Between 47 and 52 months of service. (Round z values to 2 decimal places, probability calculations to 4 decimal places and your final answer to 4 decimal places.)

    
c. Within ± 3 months of the mean life. (Round z values to 2 decimal places, probability calculations to 4 decimal places and your final answer to 4 decimal places.)

Explanation / Answer

for normal distirbution z score =(X-mean)/std deviation

a)hence P(T<40) =P(Z<(40-48)/6) =P(Z<-1.33)=0.0918

b)

P(47<T<52) =P(-0.17<Z<0.67)=0.7486-.4325 =0.3161

c)

P(48-3<T<48+3)=P(-3/6<Z<3/6)=0.6915-0.3085 =0.3830

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