Question

Derek used a random sample of seven 7th graders to determine that 14 out of 20 7th graders have cell phones. If there are 150 7th graders in the school, estimate the number of 7th graders who have cell phones.

Answer 1

To estimate the number of 7th graders who have cell phones, we can use the proportion of 7th graders who have cell phones in the random sample. Given that 14 out of 20 7th graders in the sample have cell phones, we can set up a proportion to find the estimated number of 7th graders with cell phones in the whole school. Solving the proportion gives an estimate of approximately 105 out of 150 7th graders having cell phones.

Step-by-step explanation:

To estimate the number of 7th graders who have cell phones, we can use the proportion of 7th graders who have cell phones in the random sample. Derek found that 14 out of 20 7th graders in the sample have cell phones.

We can set up a proportion using this information:

(number of 7th graders with cell phones) / (total number of 7th graders) = (number of 7th graders with cell phones in the sample) / (total number of 7th graders in the sample)

Plugging in the given values, we have:

(number of 7th graders with cell phones) / 150 = 14 / 20

Solving for the number of 7th graders with cell phones, we get:

number of 7th graders with cell phones = (14 / 20) x 150 = 105

Therefore, we can estimate that approximately 105 out of 150 7th graders in the school have cell phones.