Fandango is experiencing record high sales and rentals for films over the course of the pandemic. They are trying to compete on the VOD scene by offering frequent sales on new “Home Theater" releases of films. On average, these films rent for around $19.99 per film with the premium films. There is a standard deviation for the rental prices of $2.50. Fandango wants to have lower prices but not low enough to be in the bottom 5% of rental prices. They utilize random samples of 10 services for a particular film to investigate. What should the lowest price be so that they are not in the bottom 5%?
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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