It is known that, under standard conditions, \(12 \%\) of light bulbs from a certain manufacturer have a defect. A quality improvement process has been implemented, and a random sample of 200 light bulbs produced after the improvements was selected. It was found that 15 of the 200 light bulbs were defective.
State one assumption needed in order to use a binomial model for the number of defective light bulbs in the sample.
Test, at the \(5 \%\) significance level, whether the proportion of defective light bulbs has decreased under the new process. [0pt]
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The histogram shows information about the lengths, \(l\) centimetres, of a sample of worms of a certain species.
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The number of worms in the sample with lengths in the class \(3 \leqslant l < 4\) is 30 .
Find the number of worms in the sample with lengths in the class \(0 \leqslant l < 2\).
Find an estimate of the number of worms in the sample with lengths in the range \(4.5 \leqslant l < 5.5\). [0pt]
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