Question

6. Suppose that wedding costs in the Caribbean are normally distributed with a mean of $6000 and a standard deviation of $735. Estimate the percentage of Caribbean weddings that cost (a) between $5265 and $6735. % (b) above $6735. % (c) below $4530. % (d) between $5265 and $7470. %

Answer 1

To solve this problem, the first thing we must do is find the Z-Score of the given costs: $5265 , $6735 , $4530 ,and $7470

Then we proceed to find the percentages for each interval based on the graph

z-score for $5265 )

`Z_(5265)=(5265-6000)/(735)=-1`

z-score for $6735 )

`Z_(6735)=(6735-6000)/(735)=1`

z-score for $4530 )

`Z_(4530)=(4530-6000)/(735)=-2`

z-score $7470 )

`Z_(7470)=(7470-6000)/(735)=2_{}`

now, let's analyze the intervals

a ) between $5265 and $6735

This interval goes from (μ-σ) to (μ+σ)

if we look at the graph we find that this corresponds to a percentage of 68%

b) above $6735

This corresponds to what is to the right of (μ+σ)

This is a percentage of 16%

`(100-68)/(2)=(32)/(2)=16`

c ) below $4530

This corresponds to what is to the left of (μ-2σ)

This is a percentage of 2.5%

`(100-95)/(2)=(5)/(2)=2.5`

d ) between $5265 and $7470

This interval goes from (μ-σ) to (μ+2σ)

This is a percentage of 81.5%

`\begin{gathered} 100-(100-68)/(2)-(100-95)/(2) \\ =100-16-2.5 \\ =81.5 \end{gathered}`