Problem 23SE

The mean duration of television commercials is 75 seconds with standard deviation 20 seconds. Assume that the durations are approximately normally distributed to answer the following.

a What percentage of commercials last longer than 95 seconds?

b What percentage of the commercials last between 35 and 115 seconds?

c Would you expect commercial to last longer than 2 minutes? Why or why not?

Solution

Step 1of 3

The given mean duration is

And the standard deviation is

a) We have to find percentage of commercials is more than 95 seconds

Now we have to find P(X>95)

Then Z=(

=(95-75)/20

=1

Now find the area to the right of z=1 from the tables

Then P(Z>1)=1-0.8413

=0.1587

=15.87%

Hence the percentage of commercials is more than 95 seconds is 15.87%