A chemical reaction is run in which the usual yield is 70. A new process has been devised that should improve the yield. The claim is that it produces better yields more than 90% of the time. Let p be the probability of an increased yeild. The new process is tested 65 times. Let X denote the number or trials in which the yeild exceeds the 70 threshold. Is the normal approximation appropriate for this problem? If we agree to accept the claim(new process produces better yeilds more than 90% of the time) as true if X is at least 62 what is the probability that we accept the claim as true assuming p is equal to .9? How does the probability of seeing X equal at least 62 change if p is auctally only .85? How does this change if p is auctally .95?
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!
A chemical reaction is run in which the usual yield is 70. A new process has been devised that should improve the yield. The claim is that it produces better yields more than 90% of the time. Let p be the
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
