Movie trailers are designed to entice audiences by showing s

Movie trailers are designed to entice audiences by showing scenes from coming attractions. Several trailers are usually shown in a theater before the start of the main movie. Suppose that the duration of a movie trailer is normally distributed with mean 100 seconds and standard deviation 20 seconds. Find the probability that a randomly selected trailer lasts exactly 2 minutes. Find the probability that a randomly selected trailer lasts less than 2 minutes.

Solution

a)

The probability of exactly 2 minutes is 0. [ANSWER, 0]

This is so because we need an area to get a probability, but we need an interval (not just a point) to get an area.

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 2*60 =   120 seconds      
u = mean =    100      
          
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) / s =    1      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1   ) =    0.841344746 [ANSWER]