How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?
2 answers:
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Answer:
a) X Freq. Rel Freq.
__________________________
0 7 (7/58) = 0.121
1 10 (10/58)=0.172
2 13 (13/58) =0.224
3 14 (14/58)=0.241
4 6 (6/58)=0.103
5 3 (3/58)=0.052
6 3 (3/58)=0.052
7 1 (1/58) =0.017
8 1 (1/58)=0.017
_________________________
Total 58 1.00
b)
Step-by-step explanation:
Assuming this question: Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:
2,1,2,4,0,1,3,2,0,5,3,3,1,3,2,4,7,0,2,3,
0,4,2,1,3,1,1,3,4,2,3,2,2,8,4,5,1,3,1,
5,0,2,3,2,1,0,6,4,2,1,6,0,3,3,3,6,2,3
(a) Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch. (Round your relative frequencies to three decimal places.)
For this case first we order the dataset on increasing way and we got:
0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 3 3 3 3
4 4 4 4 4 4
5 5 5
6 6 6
7
8
And we can construct the following table:
X Freq. Rel Freq.
__________________________
0 7 (7/58) = 0.121
1 10 (10/58)=0.172
2 13 (13/58) =0.224
3 14 (14/58)=0.241
4 6 (6/58)=0.103
5 3 (3/58)=0.052
6 3 (3/58)=0.052
7 1 (1/58) =0.017
8 1 (1/58)=0.017
_________________________
Total 58 1.00
(b) What proportion of batches in the sample have at most four nonconforming transducers? (Round your answer to three decimal places.)
For this case this proportion would be: