Q- For a sample of washers produced by a machine is normally distributed with mean inside diameter is 5.02 mm and the standard deviation is 0.05 mm. The required diameter is 4.96 to 5.08 mm, otherwise the washers are considered defective. Determine:
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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Q,- For a sample of washers produced by a machine is normally distributed with mean
inside diameter is 5.02 mm and the standard deviation is 0.05 mm. The required diameter
is 4.96 to 5.08 mm, otherwise the washers are considered defective. Determine:
a- Percentage of defective washers.
b- Probability of washers with a diameter more than 3.5 mm.
Q2-
A- A machine in refinery breaks down an average of 3 times per month. Using
Poisson probability distribution formula, find the probability that during the next
month this machine will have:
1- Exactly 2 breakdowns.
2- at most 1 breakdown.
B- Product of machine is 15% defective. By using binomial distribution, find the
probability of obtaining at most 2 defective items out of 20.
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