Question 836364: As the director of membership for a nationally renowned art museum, it is your job
to increase the number of members and the quality of the membership experience.
You’ve been wonderfully successful in recent years—membership has reached well
into the thousands. You have also recently made a greater push for data‐driven
decision‐making regarding membership strategies. As such, you have begun more
systematically collecting and rigorously analyzing data.
Of your 7,120 members, you know the following:
• 59% are women
• Of the women, 62% have income equal to or less than $100,000
• Of the men, 45% have income equal to or less than $100,000
• Of the women, 72% are married
• Of the men, 86% are married
Of those who make more than $100,000, what percentage is female?
Assumption: Assume that your members’ annual income is normally distributed with mean =$89,000 and standard deviation = $17,000.
My solution: Is the following solution correct? Please validate?
No of Women members who make more than $100,000 are: 1596 (Taking the data from pre-work)
No of Men Members who make more than $100,000 are: 1605 (Taking the data from pre-work)
Assumptions:
Members annual income is normally distributed with mean = 89000 and standard deviation =17000.
Before we proceed to find the answer to the question, first we need to calculate the z-score.
z= (x-μ)/σ
z= (100000-89000)/17000
z = 0.6470588235294118
Looking up the table A2 given in Triola book, the z score of 0.65 corresponds to .7422 which is the cumulative area from the left.
The total area of under a bell curve would be 1 and we are looking for members making more than 100000 would be 1 - .7422 = 0.2578 which would be 25.78%.
The Ratio of women who make more than $100,000 are 1596/3201 (Men making more than 100,000 +Women making $100,000) = 0.4985941893158388
After calculating the z-score, the % of people making more than $100,000 are 25.78. Which
is ( 25.78) * 3201 = 825.2178
Based on the ratio, the No of Female making more than $100,000 would be = 412.6089
The % of female making more than %100,000 would be 412.6089/3201 = 0.1289 = 12.89%.
Answer by psbhowmick(878)   (Show Source):
|
|
|
