P1. According to the 2001 Youth Risk Behavior Surveillance by the Centers for Disease Control and Prevention, 39% of the 10th-graders surveyed said that they watch three or more hours of television on a typical school day. Assume that this percentage is true for the current population of all 10th-graders. What is the probability that 86 or more of the 10th-graders in a random sample of 200 watch three or more hours of television on a typical school day? 78 85.5 0 1.09 The required probability 5- 3621.1379 P2. After a general culture test, it is observed that the scores obtained follow a distribution with an N distribution (65, 18). It is desired to classify the examinees into three groups (low general culture, acceptable general culture, excellent general culture) so that there is in the first 20% population, 65% the second and 15% in the third. What should be the scores that mark the passage from one group to the other? P3. Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15. a) Determine the percentage of the population that would obtain a coefficient between 95 and 110. b) In a population of 2500 individuals, how many individuals are expected to have a coefficient greater than 125? P4. Entomologists are often interested in studying the effect of chemical attractants (pheromones) on insects. A common technique is to release several insects at an equal distance from the fermone under study and from a substance without effect (control). If the pheromone has an effect, more insects will be directed towards it instead of heading towards control. If there is no effect, an insect will head towards one of the two possibilities with equal probability (that is, the probability that the insect is directed towards the pheromone is 0.5). In an experiment 5 insects are released. Calculate the following probabilities assuming that the pheromone has no effect. a. P (the five insects are directed towards the pheromone) b. P (exactly four insects are directed towards the pheromone) c. P (at least 1 insect is directed towards the pheromone) The level of potassium present in the blood of an adult person is normally distributed with mean 3.8 and standard deviation 0.2. A person is chosen at random: a) What is the probability that the person's potassium level is greater than 4.1? b) If the potassium level is less than 3.4, it is said that the person suffers from hypocalcemia. What is the probability that a person suffers from this disease? c) What is the probability that the potassium level is greater than 3.25 but less than 3.752 d) People with the lowest 15% of potassium level will be subjected to a diet to raise the level. What should be the maximum level of potassium required to be submitted to the diet? e) People with the 10% highest level of potassium will be subjected to a diet to lower the level. What should be the minimum level of potassium required to be submitted to the diet? P5. In a clinical study it was determined that 1 in 5 people suffer from mental illness. 30 people were randomly selected: a) What is the probability that 7 of these people suffer from mental illness? b) What is the probability that at least 8 of these people do not suffer from mental illness? c) What is the probability that at most 6 suffer from mental illness? P6. In the Framingham study about factors that affect heart disease, a large number of healthy men were followed for a period of 16 years. It was found that initially the distribution of cholesterol levels in men was Normal with mean = 224 and with standard deviation a = 48 a) A person with a cholesterol lower than 200 is considered as one with low risk of having cardiac complications. What percentage of men will be at low risk? b) If the person's cholesterol is greater than 250 then they will have heart problems in the future. What percentage of men will have heart problems? c) Men who have the 5% higher cholesterol will be subjected to a diet, to lower their cholesterol and avoid having heart problems in the future. What will be the maximum cholesterol level allowed to NOT be subjected to the diet?