Question

Temperature transducers of 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 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 41 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 non-conforming transducers in a batch. (Round your relative frequencies to three decimal places.)
b. What proportion of batches in the sample have at most four non-conforming transducers? (Round your answer to three decimal places.)

Answer 1

Answer:

a.

Number:      0,    1,       2,     3,      4,       5,    6,    7,     8

Frequency:  6,    12,     13,     15,     5,      3,     3,    1,    1

b. The proportion of the batches that have at most is 0.864

Step-by-step explanation:

a. The given data are;

2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3

0 4 2 1 3 1 1 3 4 1 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

The frequencies are;

x     fx  

0     6

1      12

2     13

3      15

4      5

5      3

6      3

7       1

8       1

The relative frequency are;

x     Rfx  

0   0.102

1   0.203

2   0.220

3   0.254

4   0.085

5   0.051

6   0.051

7   0.017

8   0.017

b. The proportion of the batches that have at most 4 is given as follows;

The number of the batches that have at most 4 = 6 + 12 + 13 + 15 + 5 = 51

Therefore, the proportion of the batches that have at most 4 = 51 / 59 = 0.864.