solve the problems completely

Direction: Solve the problems completely. 1. Suppose that x, the monthly salaries of the employees in a certain factory, is known to form a normal distribution with a mean of P 13,500 and a standard deviation of P 2,800.00. A random sample of 20 factory workers will be taken. a. What is the probability that the sample mean is less than P 12,000? b. What is the probability that the sample mean is greater than F 13,000? (2. What is the probability that the random sample will provide a mean within P 1,500 of the population mean? {1. What is the probability that the random sample will provide a mean within P 1,000 of the population mean? 2. For the rst summative test in mathematics of grade 11 students in a certain senior high school, the mean grade is 82 with a standard deviation of 13. A random sample of 30' students will be taken. a. What is the probability that the sample mean is less than 75? b. What is the probability that the sample mean is greater than 90? c. What is the probability that the sample mean within is units ofthe population mean