Read and answer the following problems. Show all necessary solutions. 1. A population has a mean of 87 and a standard deviation of 12.5. What is the probability that the mean of a random sample with size 40? a. is greater than 80? b. is lesser than 78? c. falls between 84 to 90? 2. A population has a mean age of 37 with a standard deviation of 12. What is the probability tham the mean age of the sample with size 31 falls between 34 and 38? 3. Suppose that the average amount of saturated fat in a serving of breakfast cereals is 23.5 grams and a standard deviation of 2.8 grams. If a person eats breakfast cereal every day for 1 month, find the probability that the average amount of saturated fat he/she gets from eating the cereal is less than 20 grams. 4. The local pizza parlor prepares more than a hundred of pizzas a day, and the weights may var The mean weight is 485 grams. Assume that the standard deviation of the weights is 19 gram and the sample of 45 pizzas is to be randomly selected. What is the probability that the samp mean will have a weight heavier than 490 grams? 5. A medical study claimed that pain reliever of a certain brand will take effect in an average o minutes after taking the medicine with a standard deviation of 1.2 minutes. Fifty persons wl have taken this brand of pain reliever were chosen. Find the probability that the average tim took for the medicine to take effect among the random sample is less than 10 minutes.