For a single randomly selected movie, find the probability that this movie's production cost is between 54 and 57 million dollars. For the group of 48 movies, find the probability that the average production cost is between 54 and 57 million dollars.
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 average production cost for major movies is 58 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 48 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible.
- What is the distribution of XX? XX ~ N(Correct,Correct)
- What is the distribution of ¯xx¯? ¯xx¯ ~ N(Correct,)
- For a single randomly selected movie, find the probability that this movie's production cost is between 54 and 57 million dollars.
- For the group of 48 movies, find the probability that the average production cost is between 54 and 57 million dollars.
- For part d), is the assumption of normal necessary? YesNo
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