Problem 1
To find the sample mean, we simply add up all the 40 items and then divide by 40
I will add up the values row by row, and then add up the subtotals to get the grand total
row1: 39+31+38+40+29 = 177
row2: 32+33+39+35+32 = 171
row3: 32+27+30+31+27 = 147
row4: 30+29+34+36+25 = 154
row5: 30+32+38+35+40 = 175
row6: 29+32+31+26+26 = 144
row7: 32+26+30+40+32 = 160
row8: 39+37+25+29+34 = 164
Add up the subtotals: 177+171+147+154+175+144+160+164 = 1292
Divide this over 40: 1292/40 = 32.2
So the sample mean is therefore 32.2
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To find the proportion of defective items, we count the number of times a value less than 26 shows up. That happens exactly two times. The first in row 4 (at the end of this row) is where a 25 shows up. Another copy of 25 shows up in row 8 (bottom row). There are no other values that are less than 26.
Divide this count (2) over the total sample size (40) and we get 2/40 = 1/20 = 0.05
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In summary, 32.2 will go in the first box while 0.05 will go in the second box.
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Problem 2
There are 4 values we want (2,3,5,7) out of 8 total (1,2,3,4,5,6,7,8) so 4/8 = 0.50 = 50% is the theoretical probability
This is the list of values given to us (I broke it up to help make the numbers more readable)
3, 4, 5, 2, 7
1, 3, 7, 2, 6
2, 1, 7, 3, 6
1, 8, 3, 5, 6
Of that list, the primes {3, 5, 2, 7, 3, 7, 2, 2, 7, 3, 3, 5} show up. There are 12 primes in this list out of 20. So the experimental probability is 12/20 = 3/5 = 0.60 = 60%
Therefore, the answer that goes in the "experimental probability" box is 60. The answer that goes in the second box is not 50%. I think your teacher is aiming for "10" to go in the second box because 60% is 10 percentage points higher than 50% (which was the theoretical probability found earlier)
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In summary, 60 will go in the first box while 10 will go in the second box.
