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20 December, 16:36

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 dа ta:

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.)

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  1. 20 December, 16:57
    0
    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.
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