The lengths of movies released this year are normally distributed with a mean of 128 minutes and a standard deviation of 15 minutes. Define Y to be the length of a movie. a) Find Pr(Y > 150). b) Find P(100< Y<140). c). An agency did a research project on the longer movies with movie length in the top tenth percentile. What is the shortest movie length being eligible in this research project?
The lengths of movies released this year are
a) Find Pr(Y > 150).
b) Find P(100< Y<140).
c). An agency did a research project on the longer movies with movie length in the top tenth percentile. What is the shortest movie length being eligible in this research project?
d) Suppose we take a sample of two movies. What's the probability that exactly one of them has the length longer than 150 minutes and another one in the middle of 100 to 140 minutes?
e). If 36 movies are randomly selected, what is the probability distribution of the average lengths of those 36 movies? (Hint, find sampling distribution of average movie length using Central Limit Theorem)
f). If 25 movies are randomly selected, please calculate the probability of the average length of those 25 movies are between 100 minutes to 140 minutes?
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