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In: Statistics and Probability

Question 2 In an integrated circuit (IC) production line, the length of ICs is known to...

Question 2
In an integrated circuit (IC) production line, the length of ICs is known to be normally distributed with a mean of 210 mm and a standard deviation of Q mm.
(a) Calculate the value of the standard deviation, Q if it is known that 18.07% of the length of ICs will be at minimum, 230 mm.
[4 marks]
(b) Calculate the probability that the length of ICs will be at least 189 mm but not more than 210 mm.
[3 marks]
Now, let us take a random sample of 30 ICs.
(c) Calculate the probability that the mean length of ICs will be at most 213.5 mm.
[3 marks]
(d) If the mean length of ICs in 30 samples is within half a standard deviation of the population mean, a production batch is considered approved. What is the probability that a production batch will be REJECTED?

Solutions

Expert Solution

To calculate the required probability we will use standard normal variate.

orchestra answered 2 years ago
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