normal distrubition

1. Let the random variable x follow a normal distribution with p = 50 and 0'2 = 64. a. Find the probability that X is greater than 60. b. Find the probability that X is greater than 35 and less than 62. c. Find the probability that x is less than 55. d. The probability is 0.2 that X is greater than what number? e. The probability is 0.05 that X is in the symmetric interval about the mean between which two numbers? 2. The tread life of Road Stone tires has a normal distribution with a mean of 35.000 miles and a standard deviation of 4,000 miles. a. What proportion of these tires has a tread life of more than 38,000 miles? b. What proportion of these tires has a tread life of less than 32,000 miles? c. What proportion of these tires has a tread life of between 32,000 and 38,000 mites? 3. Grade point averages of students on a large campus follow a normal distribution with a mean of 2.6 and a standard deviation of 0.5. a. One student is chosen at random from this campus. What is the probability that this student has a grade point average higher than 3.0? b. One student is chosen at random from this campus. What is the probability that this student has a grade point average between 2.25 and 2.75? c. What is the minimum grade point average needed for a student's grade point average to be among the highest 10% on this campus? d. A random sample of 400 students is chosen from this campus. What is the probability that at least 80 of these students have grade point averages higher than 3.0? e. Two students are chosen at random from this campus. What is the probability that at least one of them has a grade point average higher than 3.0? 4. A professor sees students during regular office hours. Time spent with students follows an exponential distribution with a mean of 10 minutes. a. Find the probability that a given student spends fewer than 20 minutes with the professor. b. Find the probability that a given student spends more than 5 minutes with the professor. c. Find the probability that a given student spends between 10 and 15 minutes with the professor