The length of time to do a complete full battery check and replacement at Insta-

Question

The length of time to do a complete full battery check and replacement at Insta-Bat is normally distributed with a mean of 18.2 minutes and a standard deviation of 3.4 minutes.

A. Determine what percentage of complete full battery check and replacements (if needed) will fall between 10 and 20 minutes.

B. What percentage of complete full battery check and replacements (if needed) will take less than 20 minutes?

C. Using your answer from B., If 1000 cars had a complete full battery check and replacement (if needed), how many would you expect to be finished in less than 20 minutes?

D. What percentage would take less than 10 minutes?

E. Management wants to offer customers a guarantee that a complete full battery check and replacement (if needed) can be completed within a certain amount of time. What number of minutes should they include in their guarantee, to be sure they are achieving their goal 99% of the time?

F. What number of minutes should they include in their guarantee, to be sure they are achieving their goal 95% of the time?

Explanation / Answer

here from normal distribution : Z =(X-mean)/std deviation

a)P(10<X<20) =P((10-18.2)/3.4<Z<(20-18.2)/3.4) =P(-2.412<Z<0.529) =0.7017-0.0079 =0.6938

hence 69.38% fall b/w 10 and 20 minutes.

b)P(X<20) =P(Z<0.529) =0.7017

hence 70.17% will take less then 20 minutes.

c)expected number =1000*0.7017 =701.7

d) P(X<10) =P(Z<2.412) =0.0079

hence 0.79%

E) for 99% time, they should give time according to 1 percentile for which z =-2.32635

hence corresponding time =18.2-2.32635*3.4 =10.29

F) for 95% , at 5 percentile z =-1.6449

hence  corresponding time =18.2-1.6449*3.4 =12.61

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