b What proportion of batches in the sample have at most six

?(b) What proportion of batches in the sample have at most six nonconforming transducers? (Round your answer to three decimal places.) PLEASE HELP ME FIGURE OUT PART B. Explain and show why it\'s that answer

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 3 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3 0 42 1 3 1 1 3 41 2 3 2 2 8 4 5 3 1 5 0 2 3 2 1 0 6 4 21 6 0 3 3 3 6 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.) Nonconforming Frequency Relative Frequency 0 200 233 233 0.083 12 2 3 4 5 5 0.05 0.05 0.017 8 0.017 (b) What proportion of batches in the sample have at most six nonconforming transducers? (Round your answer to three decimal places.) 0.783 What proportion have fewer than six? (Round your answer to three decimal places.) 0.866 What proportion have at least six nonconforming units? (Round your answer to three decimal places.) 0.217

Solution

(b) The proportion is

P(X<=6) = P(X=0)+P(X=1)+...+P(X=6) =0.05+0.05+0.083+0.233+0.233+0.2+0.117 = 0.966

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P(X<6) = P(X=0)+P(X=1)+...+P(X=5) =0.05+0.083+0.233+0.233+0.2+0.117 = 0.916

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P(X>=6) =1-P(X<6) =1-0.916 = 0.084