A group conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $26,858. Assume that the cost of a wedding is normally distributed with a mean of $26,858 and a standard deviation of $5,900.
(a) What is the probability that a wedding costs less than $20,000? (Round your answer to four decimal places.)
(b) What is the probability that a wedding costs between $20,000 and $32,000? (Round your answer to four decimal places.)
(c) What is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (Round your answer to the nearest dollar.)

The measures, using the normal distribution, are given as follow:a) Probability that a wedding costs less than $20,000: 0.1230 = 12.30%.b) Probability that a wedding costs between $20,000 and $32,000: 0.6848 = 68.48%.c) Minimum cost of the most expensive 5% of weddings: $36,564.Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:[tex]Z = \frac{X - \mu}{\sigma}[/tex]The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the wedding prices are given as follows:[tex]\mu = 26858, \sigma = 5900[/tex]The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:[tex]Z = \frac{X - \mu}{\sigma}[/tex]Z = (20000 - 26858)/5900Z = -1.16Z = -1.16 has a p-value of 0.1230.The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:[tex]Z = \frac{X - \mu}{\sigma}[/tex]Z = (32000 - 26858)/5900Z = 0.87Z = 0.87 has a p-value of 0.8078.0.8078 - 0.1230 = 0.6848.The minimum cost for a wedding to be in the most expensive 5% of the weddings is the 95th percentile, which is X when Z = 1.645, hence:[tex]Z = \frac{X - \mu}{\sigma}[/tex]1.645 = (X - 26858)/5900X - 26858 = 1.645 x 5900X = $36,564.More can be learned about the normal distribution at https://brainly.com/question/25800303#SPJ1