To select a weight loss plan, the subjects must have loss at least 6.25 pounds o

Question

To select a weight loss plan, the subjects must have loss at least 6.25 pounds once a plan enters the bottom 30%. Given the weight of threshold weight of 6.25 pounds, and using the standard normal table, determine if either of these plans meet the criteria for selection.

Plan 1 Subject Number Pounds Loss on Plan 1 Plan 2 Subject Number Pounds Loss on Plan 2 39 4.8 1 5.8 42 5.7 14 6.4 32 6.5 37 6.5 6 6.7 11 6.6 16 6.8 17 6.6 23 6.8 31 6.7 10 6.9 41 6.7 19 6.9 12 6.8 4 7 10 7 44 7.1 43 7 1 7.2 30 7.1 9 7.2 50 7.1 2 7.3 24 7.3 36 7.3 46 7.3 38 7.3 48 7.3 45 7.5 42 7.4 11 7.6 44 7.4 21 7.6 20 7.5 22 7.7 6 7.6 33 7.9 18 7.6 28 8 23 7.6 31 8 25 7.6 47 8.2 33 7.7 30 8.3 26 7.8 3 8.4 4 8 12 8.5 13 8 18 8.5 47 8 8 8.8 8 8.1 14 8.8 9 8.3 15 8.9 38 8.3 37 8.9 19 8.4 13 9.8 22 8.4 34 9.8 32 8.5 43 9.8 3 8.6 7 10.1 16 8.6 27 10.1 28 8.6 25 10.2 35 8.6 35 10.3 49 8.6 41 10.6 34 8.7 48 10.8 5 8.8 20 11 40 8.8 40 11.2 21 8.9 50 11.7 36 9.1 29 11.8 2 9.3 46 11.8 39 9.3 5 12 27 9.4 17 12.2 29 9.4 26 12.6 45 9.4 49 12.7 15 9.9 24 13.5 7 10.4

Explanation / Answer

both of these plans meet the criteria for selection

following information has been generated using ms-excel

sd is population standard deviation

we use standard normal variate z=(x-mean)/sd

here bottom 30% means P(Z<z)=0.3 and z=-0.5244

so corresponding x for bottom 30% for plan1=8.9-0.5244*4.1=6.75

so corresponding x for bottom 30% for plan2=7.98-0.5244*1=7.46

both the plans have lost weight more than 6.25

plan 1 plan 2 mean= 8.90 7.98 sd= 4.10 1.00

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