The sulfur content of commercially available dried apricots is normally distributed with an average of 1500 ppm and a standard deviation of 250 ppm. Dried apricots are selected at random a)Calculate the probability that the sulfur content of this apricot exceeds 1450 ppm. b)Find such a sulfur value of dried apricots so that 40% of dried apricots exceed this sulfur value. c)If the sulfur content of a selected dried apricot exceeds 2000 ppm, let's call it high sulfur apricot. Calculate the probability that at least 5 of 6 randomly selected dried apricots have high sulfur by approximating the normal distribution to the binomial distribution.
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!
The sulfur content of commercially available dried apricots is
a)Calculate the probability that the sulfur content of this apricot exceeds 1450 ppm.
b)Find such a sulfur value of dried apricots so that 40% of dried apricots exceed this sulfur value.
c)If the sulfur content of a selected dried apricot exceeds 2000 ppm, let's call it high sulfur apricot. Calculate the probability that at least 5 of 6 randomly selected dried apricots have high sulfur by approximating the normal distribution to the binomial distribution.
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