Temperature Transducers of a Certain Type Are Shipped in Batches

Essay

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: $$\begin{array} { l l l l l l l l l l l l l l l l l l l l } 0 & 4 & 2 & 1 & 3 & 1 & 1 & 3 & 4 & 1 & 2 & 3 & 2 & 2 & 8 & 4 & 5 & 1 & 3 & 1 \\2 & 1 & 2 & 4 & 0 & 1 & 3 & 2 & 0 & 5 & 3 & 3 & 1 & 3 & 2 & 4 & 7 & 0 & 2 & 3 \\5 & 0 & 2 & 3 & 2 & 1 & 0 & 6 & 4 & 2 & 1 & 6 & 0 & 3 & 3 & 3 & 6 & 1 & 2 & 3\end{array}$$
a. Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch.
b. What proportion of batches in the sample has at most four nonconforming transducers? What proportion has fewer than four? What proportion has at least four nonconforming units?