Question

he XO Group Inc. conducted a survey of brides and grooms married in the United States and found that the average cost of a wedding is (XO Group website, January , ). Assume that the cost of a wedding is normally distributed with a mean of and a standard deviation of . a. What is the probability that a wedding costs less than (to 4 decimals)? b. What is the probability that a wedding costs between and (to 4 decimals)? c. For a wedding to be among the most expensive, how much would it have to cost (to the nearest whole number)?

Answer 1

A. P(X<20,000) = 0.0392

B. P(20,000 < x < 30,000) = 0.488

C. Amount = $39,070

Explanation:

From XO group website

Cost of a wedding = $29,858

Mean, μ = $29,858

Standard Deviation, σ =$5,600

a. Calculating the probability that a wedding costs less than $20,000

P(X<20,000)?

First, the z value needs to be calculated.

z = (x - μ)/σ

x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

So, P(X<20,000) = P(Z<-1.76)

From the z table,

P(Z<-1.76) = 0.0392

P(X<20,000) = 0.0392

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

P(20,000 < x < 30,000)

First, the z value needs to be calculated.

z = (x - μ)/σ

When x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

When x = 30,000

z = (30,000 - 29,858)/5600

z = 0.02

P(20,000 < x < 30,000) = P(-1.76 < z <0.02) --- using the z table

P(-1.76 < z <0.02) = 0.508 - 0.0392

P(-1.76 < z <0.02) = 0.4688

P(20,000 < x < 30,000) = 0.488

c. Using the following formula, we'll get the amount it'll a wedding to be among the 5% most expensive

z = (x - μ)/σ where x = amount

Make x the subject of formula

x = σz + μ

Fist we need to get the z value of 5%

z0.05 = 1.645

x = σz + μ becomes

x = 5600 * 1.645 + 29,858

x = $39,070

Amount = $39,070