Question 52·Easy·Inference from Sample Statistics and Margin of Error
There are 80 members in the chess club. A random sample of the members was surveyed and asked whether they plan to attend the regional tournament. Of those surveyed, 35% responded that they plan to attend.
Based on this survey, which of the following is the best estimate of the total number of chess club members who plan to attend the regional tournament?
For questions that ask you to estimate a total from a sample percentage, assume the sample percentage applies to the whole group. Convert the given percent to a decimal or fraction, multiply it by the total population size, and then match your result to the closest answer choice. Be careful not to confuse the percent itself with the actual number of people, and always check that your result is a reasonable portion of the total.
Hints
Use the sample percentage
The question tells you the percent of surveyed members who plan to attend. How can you use that percentage to estimate for all 80 members?
Convert percent to decimal
Rewrite as a decimal or fraction so you can multiply it by 80.
Set up the calculation
You want “35% of 80.” What multiplication expression represents “35% of 80”?
Desmos Guide
Calculate 35% of 80
In Desmos, type 0.35 * 80 (or (35/100) * 80) and look at the numerical output. That value is the estimated number of club members who plan to attend the tournament.
Step-by-step Explanation
Interpret what the 35% represents
The survey found that 35% of the sampled members plan to attend. On SAT questions like this, you are usually expected to assume that this same percentage applies to the entire group of 80 club members.
Convert the percentage to a decimal
To use the percentage in a calculation, convert to a decimal:
Apply the percentage to the total number of members
Multiply the total number of members by this decimal to estimate how many plan to attend:
This product gives the estimated number of chess club members who plan to attend the regional tournament.
Compute and match to the answer choices
Now compute the product:
So the best estimate of the total number of members who plan to attend the regional tournament is 28, which corresponds to choice B).