An industrial process produces batches of Items whose masses have a normal distribution with mean p and variance o. When the process is working correctly. p-m. From each batch a single item is selected at random and tits mass Is determined. If this mass is less than m - 30, or is greater than m+ 30, then the production process is halted and the machinery is inspected. Given that the process is working correctly, calculate, correct to 3 decimal places, the probability that the process Is halted for the first time after fewer than 20 batches have been produced.

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An Industrial process produces batches of tems whose masses have a normal distribution with mean p
and varlance o. When the process is working correctly, u- m. From each batch a single item is selected
at random and its mass Is determined. Ir this mass is less than m - 30, or is greater than m + 30, then
the production process is halted and the machinery is inspected. Given that the process is working
correctly, calculate, correct to 3 decimal places, the probability that the process Is halted for the first
time after fewer than 20 batches have been produced.
Transcribed Image Text:An Industrial process produces batches of tems whose masses have a normal distribution with mean p and varlance o. When the process is working correctly, u- m. From each batch a single item is selected at random and its mass Is determined. Ir this mass is less than m - 30, or is greater than m + 30, then the production process is halted and the machinery is inspected. Given that the process is working correctly, calculate, correct to 3 decimal places, the probability that the process Is halted for the first time after fewer than 20 batches have been produced.
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