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2. The average number of acres burned by forest and range fires in a large New Mexico county is 4,300 acres per year, with a standard deviation of 750 acres. The distribution of the number of acres burned is normal. What is the probability that between 2,500 and 4,200 acres will be burned in any given year?
Diodes used on printed circuit boards are produced in lots of size 1000 . taking samples of size 64 from each lot. If the nominal value of the fraction nonconforming is p-0.1, determine the parameters of the appropriate control chart. What is the minimum sample size that would give a positive lower control limit for this chart? We wish to control the process producing these diodes by
math   Statistics-And-Probability   
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Answer #1

2:

Here we have

μ 4300, σ 750

The z-score for X = 2500 is

X-μ 2500-4300 750

The z-score for X = 4200 is

X-μ 4200-4300 0.13 750

The required probability is

P(2500 < x < 4300)-P(-24 < z <ー0.13)-P(z <-0.13)-P(z < -2.4) 0.4401

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