Question

label and answer all parts

Bonnaroo is a four-day music festival held every summer in Tennessee since 2002. Suppose the mean attendance for the festival is 81,523 people with a standard deviation of 3,233. Assume the number of people attending the festival is normally distributed. Use the Empirical Rule to answer parts a c: a. Organizers of the festival can expect between and people to attend the festival 68% of the time. b. Approximately c. If attendance this year is in the top 2.5%, then the attendance would be d. Mumford & Sons was one of the headline acts this year, and organizers anticipated a high attendance. An attendance of 95,000 people would be % of festivals will be attended by less than 91,222 people. or more people. standard deviations 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

Solution:-

a) Organisers of the festival can expect between 78290 and 84756 people to attend the festival 68% of the time.

According to empirical rule 68% of the data points lie between 1 standard deviation.

b) Approximately 99.85% of festivals will be attended by less than 91,222.

According to empirical rule 99.7% of the data points lie between 3 standard deviation.

x = 91222

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = 3.0

P(x < 3.0) = 1 - 0.0015

P(x < 3.0) = 0.9985

c) If the attendance this year is in the top 2.5%, then attendance would be 87989 or more people.

According to empirical rule 95% of the data points lie between 2 standard deviation.

d) An attendance of 95000 people would be 4.17 standard deviations above the mean.

x = 95000

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = 4.17