For the past ten years, grades on the final exam in Mr. Statmanâs statistic course have been normally distributed with a mean of µ = 75 and a standard deviation of Ï = 15. Mr. Statman has a current class with 50 students. Let us predict some outcomes on the final exam for that class.
a) Draw a normal distribution. Include the mean and two standard deviations. Complete this sentence using the Empirical Rule: Approximately, 95% of students will score between _ and __ on the final exam.
b) Shade in the A range (90 and above) on your distribution in part a. Find the probability that a randomly selected student makes an A on Mr. Statmanâs final exam. How many of the 50 students do we expect to make an A?
c) Suppose that we randomly select 5 students from the class and AVERAGE their final exam scores. The Central Limit Theorem indicate that the average of the 5 students will fall somewhere in a Normal Distribution with = and = . Complete this sentence using the Empirical Rule: Approximately, 95% of the time the average of 5 random students will fall between _ and __ on the final exam.
d) Find the probability that the average of the 5 students is an A average (90 and above).
e) Letâs do the same thing that we did in parts c and d, except for the entire class of 50. The Central Limit Theorem indicate that the average of the 50 students will fall somewhere in a Normal Distribution with = and = . Complete this sentence using the Empirical Rule: Approximately, 95% of the time the average of 50 random students will fall between _ and __ on the final exam.
f) Find the probability that the average of the 50 students is an A average (90 and above).
g) Find the following probabilities (you redoing parts b, d, and f, but with a C instead of an A) :
A) P(a randomly selected student makes a C on the final exam) = __
B) P(a sample of 5 randomly selected students make a C average of the final exam) = _
C) P(the class average of all 50 students will be a C average)
Sample Solution
roduce an acute psychotic reaction in non-schizophrenic people who consume marijuana, although this usually goes away as the drug wears off. Marijuana smoke contains a number of harmful chemicals that lead up to damage of the bronchial passages and the lungs. Regular smokers are more likely to have persistent coughs, trouble breathing, and produce excess mucus from their throats. The Journal of Internal medicine has stated that smoking marijuana âhas some significant similarities to that of tobacco smoking.â Consuming marijuana can increase the heart rate by almost 50 bpm, which can last for over three hours. This overworks the heart and can eventually lead to heart attacks. Research from the Journal of the American stated that regular marijuana use can not only lead to a higher risk of a heart attack, but cause issues such as heart rhythm disorders and strokes, even in younger people who are not at risk for heart disease. One of the most concerning risks of long-term effects of marijuana consumption comes from pregnant women. When a woman is pregnant and is using marijuana, she puts the child at risk for long lasting harm to the memory. On top of potential harm during pregnancy, cannabis can be transmitted through breast milk and be passed to the infant during breastfeeding. Research has been spotty on how much cannabis affects unborn and nursing babies, but mothers to be are still advised to stay away from any foreign substances. There is a risk of addiction to consistent marijuana users, but the risk highly increases when the consumer is an adolescent. 30% of adults who use marijuana regularly are addicted, but in adolescents the likelihood of addiction is 4 to 7 of that. Marijuana use disorder becomes an addiction when a person still feels the need to use the drug even though it interferes with certain aspects of their life. Withdrawals also pose a real problem and lead to health issues such as loss of appetite, depression, insomnia, and anxiety. There is always an alternative solution to a problem rather than handing your life over to drugs. Marijuana has been legalized for recreational use in 10 different states leading to much more substance abuse within the country. It is evident that adolescents who consume this drug are at a much higher risk of mental disorders, memory loss, poorer education, and medical issues.>
roduce an acute psychotic reaction in non-schizophrenic people who consume marijuana, although this usually goes away as the drug wears off. Marijuana smoke contains a number of harmful chemicals that lead up to damage of the bronchial passages and the lungs. Regular smokers are more likely to have persistent coughs, trouble breathing, and produce excess mucus from their throats. The Journal of Internal medicine has stated that smoking marijuana âhas some significant similarities to that of tobacco smoking.â Consuming marijuana can increase the heart rate by almost 50 bpm, which can last for over three hours. This overworks the heart and can eventually lead to heart attacks. Research from the Journal of the American stated that regular marijuana use can not only lead to a higher risk of a heart attack, but cause issues such as heart rhythm disorders and strokes, even in younger people who are not at risk for heart disease. One of the most concerning risks of long-term effects of marijuana consumption comes from pregnant women. When a woman is pregnant and is using marijuana, she puts the child at risk for long lasting harm to the memory. On top of potential harm during pregnancy, cannabis can be transmitted through breast milk and be passed to the infant during breastfeeding. Research has been spotty on how much cannabis affects unborn and nursing babies, but mothers to be are still advised to stay away from any foreign substances. There is a risk of addiction to consistent marijuana users, but the risk highly increases when the consumer is an adolescent. 30% of adults who use marijuana regularly are addicted, but in adolescents the likelihood of addiction is 4 to 7 of that. Marijuana use disorder becomes an addiction when a person still feels the need to use the drug even though it interferes with certain aspects of their life. Withdrawals also pose a real problem and lead to health issues such as loss of appetite, depression, insomnia, and anxiety. There is always an alternative solution to a problem rather than handing your life over to drugs. Marijuana has been legalized for recreational use in 10 different states leading to much more substance abuse within the country. It is evident that adolescents who consume this drug are at a much higher risk of mental disorders, memory loss, poorer education, and medical issues.>
