Question

1. Answer the following by SHOWING ALL YOUR WORK

A) Suppose there was a class of 200 students with a mean class average of 63%. I then select from this class all students on the honor roll, which amounts to 53 students. Would you expect their average to be the same? Why or why not?

B) According to the label on a drink bottle, the bottle should contain 500 mL of product. Currently, the filling machine is set to a mean volume of 502 mL and a standard deviation of 1.5 mL. If too many cans are under-filled, they risk losing customers, but if the can surpasses 505 mL of fill, there will be spillover when the bottle is capped, wasting product. Does the company need to recalibrate the machine?

Answer 1

a)

YES, we expect their average to be same 63%

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µ =    502                              
σ =    1.5                              
we need to calculate probability for ,                                  
P (   500   < X <   505   )                  
=P( (500-502)/1.5 < (X-µ)/σ < (505-502)/1.5 )                                  
                                  
P (    -1.333   < Z <    2.000   )                   
= P ( Z <    2.000   ) - P ( Z <   -1.333   ) =    0.9772   -    0.0912   =    0.8860 (88.60%)

need to recalibrate as proportion of cans outside > 10%

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THANKS

revert back for doubt

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