Question 1:
A middle school has 450 students. In a random sample of 100 students, 8 students indicated that they have traveled outside the United States. Predict the number of students at the middle school who have traveled outside the United States.
Question 2:
In a random sample of 400 watches, 3 are defective. Out of a total of 10,500 watches, how many would you expect to be defective based on this sample data?
Answer 1:
To predict the number of students at the middle school who have traveled outside the United States, we can use the concept of proportions.
First, we can calculate the proportion of students in the random sample who have traveled outside the United States:
proportion in sample = 8/100 = 0.08
We can then use this proportion to estimate the number of students who have traveled outside the United States in the entire middle school:
number of students = proportion in sample x total number of students
number of students = 0.08 x 450
number of students = 36
Therefore, we can predict that 36 students at the middle school have traveled outside the United States.
Answer 2:
We can use the proportion of defective watches in the sample to estimate the proportion of defective watches in the entire population.
proportion in sample = 3/400 = 0.0075
We can then use this proportion to estimate the number of defective watches in the entire population:
number of defective watches = proportion in sample x total number of watches
number of defective watches = 0.0075 x 10,500
number of defective watches = 79
Therefore, based on this sample data, we would expect approximately 79 watches out of 10,500 to be defective.
are you sure the second one is correct?
I apologize, I made an error in the calculation.
The correct solution for Question 2 is:
proportion in sample = 3/400 = 0.0075
We can then use this proportion to estimate the number of defective watches in the entire population:
number of defective watches = proportion in sample x total number of watches
number of defective watches = 0.0075 x 10,500
number of defective watches = 78.75
Since you cannot have a fraction of a watch, we can round the answer to the nearest whole number.
Therefore, based on this sample data, we would expect approximately 79 watches out of 10,500 to be defective.
Answer 1:
To predict the number of students at the middle school who have traveled outside the United States, we can use the concept of proportion.
Step 1: Calculate the proportion of students in the sample who have traveled outside the United States.
Proportion = Number of students who have traveled outside the US / Total number of students in the sample
= 8 / 100
= 0.08
Step 2: Use the proportion to estimate the number of students at the middle school who have traveled outside the United States.
Estimated number = Proportion * Total number of students at the middle school
= 0.08 * 450
= 36
Therefore, based on the sample data, we would predict that approximately 36 students at the middle school have traveled outside the United States.
Answer 2:
To estimate the number of defective watches based on the sample data of 400 watches, we can use the concept of proportion.
Step 1: Calculate the proportion of defective watches in the sample.
Proportion = Number of defective watches / Total number of watches in the sample
= 3 / 400
= 0.0075
Step 2: Use the proportion to estimate the number of defective watches out of a total of 10,500 watches.
Estimated number = Proportion * Total number of watches
= 0.0075 * 10,500
= 78.75
Therefore, based on the sample data, we would expect approximately 78.75 watches out of the total 10,500 to be defective. Since we cannot have a fraction of a watch, we round this value to the closest whole number. Hence, we would expect about 79 watches to be defective.