Provide complete calculation. Don't submit only explanation.

7. Candidate A is running for office and 45% of the electorate favor her. What is the probability that among 100 randomly selected voters, at least 50% favor her? Estimate this probability by using the normal approximation to the distribution of the sample proportion. 8. Twelve astronauts performed a task under simulated weightlessness. The increase in pulse rate each measured for each astronaut. If the sample standard deviation of these measurements is 4.23, what it the probability that the sample mean exceeds 27.15? Assume that such measurements are independent following a normal distribution with mean 25. 9. Transactions at a bank window are normally distributed with mean 2.33 minutes and standard deviation 1.10 minutes. If 5 customers are in line, what is the probability that the variance of their waiting times will exceed 2.4 minutes? Assume that their transactions are independent