Researcher: We conducted an experiment where we asked people to

Question

Researcher: We conducted an experiment where we asked people to each build the same simple model. We enlisted 200 volunteers and randomly divided them into 4 groups (Groups 1–4) of 50 members each. Each volunteer was assigned to exactly one of the groups. Each member of Group 1 was given as much time as that member needed to build the model. Each member of Group 2 was given a limited amount of time in which to build the model. Each member of Group 3 was asked to build the model while wearing a blindfold, and was given as much time as needed. Each member of Group 4 was asked to build the model while wearing a blindfold, and was given a limited amount of time. The researchers found that 98% of Group 1, 46% of Group 2, 90% of Group 3, and 20% of Group 4 were able to successfully build the model.

Select for  Number blindfolded  the total number of volunteers who succeeded in building the model while wearing a blindfold, and select for  Number timed  the total number of volunteers who succeeded in building the model while given a limited amount of time, according to the information provided. Make only two selections, one in each column.

MartyMurray · Answer

Researcher: We conducted an experiment where we asked people to each build the same simple model. We enlisted 200 volunteers and randomly divided them into 4 groups (Groups 1–4) of 50 members each. Each volunteer was assigned to exactly one of the groups. Each member of Group 1 was given as much time as that member needed to build the model. Each member of Group 2 was given a limited amount of time in which to build the model. Each member of Group 3 was asked to build the model while wearing a blindfold, and was given as much time as needed. Each member of Group 4 was asked to build the model while wearing a blindfold, and was given a limited amount of time. The researchers found that 98% of Group 1, 46% of Group 2, 90% of Group 3, and 20% of Group 4 were able to successfully build the model.

Select for Number blindfolded the total number of volunteers who succeeded in building the model while wearing a blindfold, and select for Number timed the total number of volunteers who succeeded in building the model while given a limited amount of time, according to the information provided. Make only two selections, one in each column.

Each group is composed of 50 members.

So, since 50 is half of 100, the number of members of each group who succeeded in building the model is half the percentage of the members in that group who succeeded in building the model.

The volunteers who succeeded in building the model while blindfolded were all those in Group 3 and Group 4 who succeeded.

Group 3 percentage who succeeded: 90

Group 3 number who succeeded: 90/2 = 45

Group 4 percentage who succeeded: 20

Group 4 number who succeeded: 20/2 = 10

45 + 10 = 55

For  Number blindfolded , choose  55 .

The volunteers who succeeded in building the model while given a limited amount of time were all those in Group 2 and Group 4 who succeeded.

Group 2 percentage who succeeded: 46

Group 2 number who succeeded: 46/2 = 23

Group 4 percentage who succeeded: 20

Group 4 number who succeeded: 20/2 = 10

23 + 10 = 33

For  Number timed , choose 33.

Correct answer:   55 ,  33

Bismuth83 · Answer

1. Note that the number of people who succeeded in a group is equal to the percentage multiplied by 50 (total number of people in the group).

2. Groups 3 and 4 were with people who were blindfolded. The number of blindfolded people who succeeded is equal to  0.9 * 50 + 0.2 * 50 = 45 + 10 = 55 .

3. Groups 2 and 4 were with people who were timed. The number of timed people who succeeded is equal to  0.46 * 50 + 0.2 * 50 = 23 + 10 = 33 .

4. Our answer will be:   Number blindfolded - 55 and Number timed - 33  .

egmat · Answer

Happy to walk you through this one! The  key insight  is figuring out which groups belong under each column.

First, let's organize what we know.  There are  4  groups of  50  volunteers each:

- Group  1 : No blindfold, unlimited time →  98%  succeeded =  49  people
- Group  2 : No blindfold, LIMITED time →  46%  succeeded =  23  people
- Group  3 : BLINDFOLDED, unlimited time →  90%  succeeded =  45  people
- Group  4 : BLINDFOLDED, LIMITED time →  20%  succeeded =  10  people

Now match groups to columns:

Number blindfolded  (volunteers who succeeded while wearing a blindfold):
Which groups wore blindfolds? Groups  3  and  4 .
- Group  3  successes:  45 
- Group  4  successes:  10 
-  Total =  45  +  10  =  55

Number timed  (volunteers who succeeded while given limited time):
Which groups had limited time? Groups  2  and  4 .
- Group  2  successes:  23 
- Group  4  successes:  10 
-  Total =  23  +  10  =  33

Note that  Group  4  counts toward BOTH columns because those volunteers were both blindfolded AND timed.   This is the detail that trips people up — don't forget to include Group  4  in both calculations.

So the correct pair is  55  for Number blindfolded and  33  for Number timed.

Answer: 2A, 1B

The approach for this type of TPA:  first calculate each group's successes individually, then carefully read each column header to determine which groups to combine. Always check if any group satisfies both conditions — here Group  4  does.

Researcher: We conducted an experiment where we asked people to

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