The following table gives a classification of the 10,000 shareholders of Oxnard Xylophone Distributors,Inc.A few numbers are missing from the table.Given that a shareholder holding 500−999 shares is picked,there is a 0.625 probability that the shareholder will be a woman.Consequently,what is the number of men holding 1000 or more shares?
A)1,000
B)250
C)7,500
D)500

Question

The following table gives a classification of the 10,000 shareholders of Oxnard Xylophone Distributors,Inc.A few numbers are missing from the table.Given that a shareholder holding 500−999 shares is picked,there is a 0.625 probability that the shareholder will be a woman.Consequently,what is the number of men holding 1000 or more shares? 
A)1,000 
B)250 
C)7,500 
D)500

Quizplus · Accepted Answer

We know that the probability of picking a woman holding 500-999 shares is 0.625. From the table, we can see that there are 8,000 shareholders holding less than 500 shares, and 1,250 shareholders holding 500-999 shares. Let the number of men holding 1000 or more shares be x. Then, the number of women holding 500-999 shares is 0.625(1,250), or 781.25 (rounded to the nearest whole number). Therefore, the total number of women shareholders is 781.25 + 1,250 = 2,031.25. Since there are 10,000 total shareholders, the number of men shareholders is 10,000 - 2,031.25 = 7,968.75. We know that the number of men holding less than 1000 shares is 7,968.75 - x. And we also know that the number of shareholders holding 1000 or more shares is 1,500 - the sum of shareholders holding less than 1000 shares in the table. Solving for x, we get x = 500. Therefore, the number of men holding 1000 or more shares is 500.

The Following Table Gives a Classification of the 10,000 Shareholders