7. The monthly utility bills in a certain city are normally distributed, with a mean of $100 and a Standard deviation of $12. A utility bill is randomly selected. ) Find the probability that the utility bill is less than $80. O b) Find the probability that the utility bill is between $80 and $115. ") Find the probability that the utility bill is more than $115. 8. A random group of students was surveyed to determine how many months it has been since they last visited the dentist. The sample of 32 students gave a mean of 19 months. From prior studies, we can assume the population standard deviation is 4.4 months. a) Construct a 95% confidence interval for the population mean number of months. ) Construct a 99% confidence interval for the population mean number of months. c) Determine the minimum required sample size to construct a 99% confidence interval so that the sample mean is within 2 months of the population mean