The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $29,858 (XO Group website, January 5, 2015). Assume that the cost of a wedding is normally distributed with a mean of $29,858 and a standard deviation of $5600.

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?
b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?
c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

Given that XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $29,858

X is N(29,858, 5600)

Or [tex]Z=\frac{x-29158}{5600}[/tex] is N*(0,1)

We can use std normal distribution table to get the probabilities

a) The probability that a wedding costs less than $20,000 (to 4 decimals)

= [tex]P(X<20000)\\= 0.039174[/tex]

=0.0392

b) the probability that a wedding costs between $20,000 and $30,000

=[tex]0.5101-0.0392\\=0.4709[/tex]

c) For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)

=[tex]29858+1.645*5600\\=38083[/tex]