For weight loss plan 1, what is the minimum number of pounds, the upper 20% of t

Question

For weight loss plan 1, what is the minimum number of pounds, the upper 20% of the     

      subjects loss? Use the standard normal table to calculate your answer

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

Explanation / Answer

Solution:

From the given data for plan 1, we have

Mean = 8.902

SD = 2.046549

We have to find the minimum number of pounds for which upper 20% of the subjects’ loss.

The critical value Z for upper 20% area or lower 80% area is given as below:

Z = 0.841621

(By using standard normal Z table)

Now, we have to find the value X such as

X = Mean + Z*SD

X = 8.902 + 0.841621*2.046549

X = 10.62442

Required minimum number of pounds = 10.62442

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