1. The distribution of the weights of a certain type of mangoes is normally distributed with a mean of 150 grams, and standard deviation of 13 grams. A sample of 20 mangoes of this type is taken from a shipment. What is the probability that the mean of the sample is less than 135 grams?
2. The mean systolic blood pressure is 120 and the standard deviation is 8. For a medical study, a researcher wishes to select people in the middle 60% of the population based on blood pressure. find the upper and lower readings that would qualify people to participate in the study.
3. The mean systolic blood pressure is 120 and the standard deviation is 8, a) What percent of the population have systolic blood pressure above 140? b) In a sample of 500 people, how many are expected to have a systolic blood pressure above 140?
4. A survey found that 32% of book buyers are younger than 40 years old. a)If 10 book buyers are selected at random, find the probability that at least one of them is younger than 40 years old. b) If 10 book buyers are selected at random, find the probability that two of them are 40 years old or older.