Round all answers to two decimal places. 1. The school bookstore surveyed a random sample of 10 students on whether they prefer to use a metal or plastic pen. Here were the results:
metal, metal, metal, plastic, plastic, metal, plastic, plastic, plastic, plastic

a. Estimate the proportion of all students that prefer to use a metal pen. Make your thinking visible.

b. The next day, the bookstore surveyed another random sample of 10 students and found that 20% of them preferred plastic pens. Should the bookstore believe that the results from the two days reasonably represent the preferences of the student population, or should the bookstore gather more data? Explain how you know.

2. A scientist is worried about a new disease being spread by mosquitoes in an area. The scientist captures a random sample of 137 mosquitoes from the area and tests them to find out whether they carry the disease. In this sample, 22 of the mosquitoes were carrying the disease.
Using this information, the scientist uses 100 simulations of additional samples with the same proportion of disease-carrying mosquitoes from the sample to determine that the standard deviation for the proportion of mosquitoes carrying the disease is approximately 0.029.

a. Estimate the proportion of mosquitoes in the area that carry the disease, and provide a margin of error. Explain or show your reasoning.

b. Why did the scientist run the simulations to find additional possible proportions of mosquitoes in the area that carry the disease?