1)Let the random variable X follow a normal distribution with ๐= 80 and ๐2= 100. a.Find the probability that X is greater than 60. Draw a probability distribution graph.b. Find the probability that X is greater than 72 and less than 82.c. Find the probability that X is less than 55.d. The probability is 0.1 that X is greater than what number? e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?

2) Candidates for employment at a city fire department are required to take a written aptitude test. Scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. A random sample of nine test scores was taken. โขa. What is the standard error of the sample mean score?โขb. What is the probability that the sample mean score is less than 270?โขc. What is the probability that the sample mean score is more than 250?โขd. Suppose that the population standard deviation is, in fact, 40, rather than 60. Without doing the calculations, state how this would change your answers to parts (a), (b), and (c). Illustrate your conclusions with the appropriate graphs.