20% of memory chips made in a certain plant are defective.

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The discussion centers on calculating the probabilities of defective memory chips from a plant where 20% are defective. For a sample of 100 chips, the mean number of defects is 20, with a standard deviation of 4. The probability of finding at most 15 defective chips is calculated using the normal approximation, yielding a result of approximately 0.1056. The second probability, for exactly 15 defective chips, remains unresolved in the conversation. The calculations highlight the application of statistical methods to assess quality control in manufacturing.
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Problem : 20% of memory chips made in a certain plant are defective.Find the probability that in a lot of 100 randomly chosen for inspection
i) atmost 15 are defective
ii) excatly 15 are defective.
Obtain these probability using normal approximation of binomial probabilities.
Solution

Here mean = np = 100 * 0.2 = 20
S.D. = 4

there P(Z >= 15-20/4) = 0.5 - 0.3944 = 0.1056 [IS THIS CORRECT][/color]

ii) ?
 
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