The measures, using the normal distribution, are given as follow:
a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.
b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.
c) Minimum cost of the most expensive 5% of weddings: $33,564
Normal Probability Distribution
The z-score of a measure X of a variable that has to mean symbolized by and standard deviation symbolized by is given by the rule presented as follows:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z-score represents how many standard deviations 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 measure X in the distribution.
The mean and the standard deviation for the wedding prices are given as follows:
μ = 23858, σ = 5900
a) 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 - 23858)/5900
Z = -0.65
Z = -0.65 has a p-value of 0.257.
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 - 23858)/5900
Z = 1.38
Z = 1.38 has a p-value of 0.816.
0.916 - 0.257 = 0.659.
The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:
1.645 = (X - 23858)/5900
X - 23858 = 1.645 x 5900
X = $33,564.
More can be learned about the normal distribution at brainly.com/question/25800303
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