An up-and-coming musical artist is getting their first record produced at an independent studio. They send the music out to get printed with a guarantee of 400 vinyls produced each day (with a standard deviation of 12 vinyls). Over the next 10 working days, reports have come back that they have been completing 367 vinyls on average each day. What is the probability that the production is this low? Should the artist work with this studio and producer again for a future for their next album?
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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