High levels of blood sugar are associated with an increased risk of type 2 diabetes. A level higher than normal is referred to as "impaired fasting glucose." The article "Association of Low-Moderate Arsenic Exposure and Arsenic Metabolism with Incident Diabetes and Insulin Resistance in the Strong Heart Family Study" (M. Grau-Perez, C. Kuo, et al., Environmental Health Perspectives, 2017, online) reports a study in which 47 of 155 people with impaired fasting glucose had type 2 diabetes. Consider this to be a simple random sample.

a. Find a 95\% confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes.

b. Find a \(99 \%\) confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes.

c. A doctor claims that less than \(35 \%\) of people with impaired fasting glucose have type 2 diabetes. With what level of confidence can this claim be made?