The weight of heavy bottles follows the normal distribution with the mean of 32kg and the standard deviation of 5kg A)15 heavy bottles have been found, the mean weight of that 15 heavy bottles, X_15, is measured. Find the probability that X_15 lies between 31.5kg to 32.8kg. B) Z heavy bottles have been found, the mean weight of that Z bottles, X_n, is measured. Find the smallest value of Z so that P(31.8
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 weight of heavy bottles follows the
A)15 heavy bottles have been found, the mean weight of that 15 heavy bottles, X_15, is measured. Find the
B) Z heavy bottles have been found, the mean weight of that Z bottles, X_n, is measured. Find the smallest value of Z so that P(31.8<X_n<32.2)≥99
X_15 is the first number shown in the photo
X_n is the second number
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