Question

Bonnaroo is a four-day music festival held every summer in Tennessee since 2002. Suppose the mean attendance for the festival is 80,726 people with a standard deviation of 3,173. Assume the number of people attending the festival is normally distributed. Use the Empirical Rule to answer parts a - c:  

1. Organizers of the festival can expect between____and_____ people to attend the festival 68% of the time.
2. Approximately______% of festivals will be attended by less than 74,380 people.
3. If attendance this year is in the top 2.5%, then the attendance would be______ or more people.
4. Mumford & Sons was one of the headline acts this year, and organizers anticipated a high attendance. An attendance of 95,000 people would be_____ standard deviations_______ (above or below) the mean. (In the first box, you should enter the standardized value rounded to 3 decimal places. In the second box, enter one of the following two words: above or below.)

Answer 1

Organizers of the festival can expect between__77553__and__83899___ people to attend the festival 68% of the time.

For 68% it is mean +/- sd

mean = 80726

sd = 3173

For 68% it is 80726 + /- 3173

( 77553, 83899 )

Approximately__95_% of festivals will be attended by less than 74,380 people

P[ X < 74380 ] = P[ ( X - mean(X))/sd(X) ) < ( 74380 - mean(X))/sd(X) ) ]

P[ X < 74380 ] = P[ ( X - 80726)/3173 < ( 74380 - 80726)/3173 ) ]

P[ X < 74380 ] = P[ Z < -2 ]

P[ X < 74380 ] = 95%

If attendance this year is in the top 2.5%, then the attendance would be__87072____ or more people

mean + 2*sd = 80726 + 2*3173 = 80726 + 6346 = 87072

Mumford & Sons was one of the headline acts this year, and organizers anticipated a high attendance. An attendance of 95,000 people would be__4.49___ standard deviations___above____ (above or below) the mean. (In the first box, you should enter the standardized value rounded to 3 decimal places. In the second box, enter one of the following two words: above or below.)

95000 - 80726 = 14274 ( subtract mean )

14274/3173 = 4.49 ( divide by sd )