MHB Did I Multiply Correctly for Coffee Preferences?

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The discussion focuses on verifying calculations related to coffee preferences based on a contingency table of male and female coffee drinkers. The correct percentage of those surveyed who preferred regular coffee is 30%, not 0.3%. For females who preferred bold coffee, the correct percentage is approximately 22.22%. The calculations for how much coffee Dunkin’ Donuts should purchase based on preferences are confirmed to be correct, with 350 pounds each of mild and bold, and 300 pounds of regular coffee. The thread emphasizes the importance of dividing the number of individuals in a specific category by the total number in that group to find accurate percentages.
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Hi, I was wondering if someone could check to see if this problem is correct. For part "e" I originally was dividing put changed to multiplying is that correct? Thanks in advance for the help.

A researcher was interested in the type of coffee that coffee drinkers prefer. A random sample of coffee drinkers is summarized in the contingency table below:
Mild Reg Bold
Male 20 40 50
Female 50 20 20

b) What percent of those surveyed preferred regular coffee?
i have .3%

c) What percent of females preferred bold?
i have .2222%

d) What percent of those that preferred bold were female?
3.5 %

e) A buyer for Dunkin’ Donuts reviewed the table above. If she were to base her
purchase of 1000 pounds of coffee on that information, how much of each type
of coffee – mild, regular, and bold – should she buy? Explain your answer.
So far I have: she should be 35% mld and bold which equals 70%. and 30% regular. 350 pounds of mild, 350 pounds of bold, and 300 pounds of regular. :)
 
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The number of people $N$ in the sample is the sum of the males $N_M$ and the females $N_F$:

$N=N_M+N_F=(20+40+50)+(50+20+20)=110+90=200$

b) The total in the sample that prefer regular is:

$$40+20=60$$

Hence the percentage that prefer regular is:

$$\frac{60}{200}=\frac{30}{100}=30\%$$

c) The number of females that prefer bold is 20, and so the percentage of females that prefer bold is:

$$\frac{20}{N_F}=\frac{20}{90}=\frac{20\cdot\frac{10}{9}}{90\cdot\frac{10}{9}}=\frac{\frac{200}{9}}{100}=22.\bar{2}\%$$

Do you see that to find the percentage, we want to divide the number of a group that have the trait in question by the total number in that group, and get the denominator to be $100$? Of course, you can simply do the division then multiply by 100 as well.

So for part d) how many total prefer bold and how many of those are female?

You have done part e) correctly.
 

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