In 2021 a researcher took a random sample of 200 community college students. They are surveying respondents on the following 2 questions: I. Do you have a car you can regularly drive to school? II. How old were you when you started driving? 1. Which question above will result in a response that is categorical 2. A 2016 report stated that 58% of community college students have a car they can regularly drive to school. Let X = the number of students in the sample of 200 with a car. Explain why we can use the binomial distribution to model the distribution of possible responses if we assume that 58% is still the probability that a randomly selected community college student has a car they can drive to school regularly. 3. In the researcher's survey of 200 community college students, 102 had a car they could drive to school regularly. If we assume that in 2021 the probability a student has a car is still 58% what is the probability of finding 102 or fewer in a random sample of 200 students? 4. A 2012 report stated the distribution of ages at when students first get their driver's license to be normally distributed with a mean of 17.9 years and a standard deviation of 0.8 years. Use the empirical rule to explain what it means to be normally distributed. 5. Assuming the true mean age is actually still 17.9 years with a standard deviation of 0.8 years, what is the probability of finding a community college student who gets their driver's license when they are older than 19? 6. Which of the following are unusual events? Explain using the probabilities above. I. To find 102 or less students who drive to campus -> Q3. II. A student who does not get their driver's license until they are older than 19 ->Q5.

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