Temperature transducers of a certain type are shipped in batches of 50. A sample

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: 1 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 1 2 3 2 2 8 4 4 1 3 1 5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 7 1 2 2 (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.) (b) What proportion of batches in the sample nave at most four nonconforming transducers? What proportion have fewer than four? What proportion have at least four nonconforming units? (c) Draw a histogram of the data using reactive frequency on the vertical scale. Comment on its features. (Select an that apply.) There Is some positive skewness in the data. The center of the histogram is around 2 or 3. The center of the histogram is around 7. The center of the histogram is around 1. The distribution is fairly symmetric. There is some negative skewness In the data

Explanation / Answer

x frequency relative frequency

0 7 7

1 13 20

2 13 33

3 13 46

4 7 53

5 2 55

6 2 57

7 2 59

8 1 60

b)

proportion of batches for at most 4 transducers

=Total no of batches for at most 4 transducers/60

= 53/60 = 0.8833

proportion fewer than four = 46/60 = 0.7666

proportion of at least four = 14/60 = 0.2333

c)

third histogram shows correct representation

d) There is some positive skewness in the data and center lies around 2 to 3

so first and second option is correct

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