The mean length of a movie in 2014 was 121 min (http://www.randalolson.com/2014/

Question

The mean length of a movie in 2014 was 121 min (http://www.randalolson.com/2014/01/25/movies-arent-actually-much-longer-than-they-used-to-be/) Suppose that the standard deviation is 16 minutes and that the distribution of movie times is normal. (A) What is the probability that a randomly selected movie lasts more than 110 minutes? (B) Find a time such that only 20% of all movies last more than that time. (C) A theatre randomly selects 15 movies to show. What is the probability that the mean run time for the 15 movies is more than 130 minutes?

Explanation / Answer

Here let X is normal with mean 121 and standard deviation 16

Z=(X-121)/16 is standard normal distribution

So to find

A) P(X<110)= P(Z<(110-121)/16)=P(Z<-11/6)=0.0333

B) LET that time is k, so find k such that

P(X<K) =0.2

after calculation we get k=107.53

C) there is 15 movies has shown let Y be the mean time of those 15 movies having mean 121 and Variance 16*16/15

Here Z is defined as

Z=sqrt (15)*(y-121)/16 is standard normal

So the required probability is

P(Y>130)=P(Z>(130-121)*sqrt(15)/16)=0.0000001

Where value of Z calculated from table of standard normal.

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