ayout References Mailings Review View Tell me LE Shar 4. A district court judge presides over many court cases each day. Let the random variable X= the number of cases on a randomly selected day in which she declares the defendant guilty. The distribution for the random variable X is given below: # of guilty verdicts Probability 0.05 0.10 0.20 0.25 0.25 0.15 a) What is the expected value of the number of guilty verdicts in a day? b) What is the standard deviation of the number of guilty verdicts in a day? c) If we selected two days at random, what is the probability that the judge declares exactly nine defendants guilty over those two days? d) If we selected two days at random, what is the probability that the judge declares at least nine defendants guilty over those two days? 5. A public health researcher is interested in whether fast food increases the risk of childhood obesity. She obtains data on the location of every fast-food restaurant in the United States and a county-level measure for the rate of childhood obesity per 100,000 children. Suppose she determines that the correlation between childhood obesity and the number of fast-food restaurants in the county is r=0.57. She also obtains the following information about the mean and standard deviation of each variable: Fast food restaurants Childhood obesity rate per 100K Mean=25.3 Mean=18.5 Standard Deviation=12.4 Standard Deviation=10.7 a) Write down a regression formula to explain the relationship between fast food and childhood obesity. Be sure to label which is the "y" variable and which is the "x" variable. b) Calculate the regression line using the information provided above. c) Interpret the values for bo and b1 Suppose a county is considering allowing a new fast-food chain of 8 restaurants to open. Based on your estimates thus far, what is your prediction for how the opening of these establishments would affect the childhood obesity rate? Be specific