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1. Recall that we write X ~ N(µ,0) for a random variable X whose values x follow a normal distribution with mean u and standard deviation ơ. Use a standard normal distribution table to find th following probabilities. Explain your answers, and illustrate each of your answers graphically: A. For Z - N(0,1) : P(z< 0.64) = ? P(- 1.32 < z< +1.32) = ? P(z> - 1.56) = ? P(0.59 < z<1.89) = ? b. d. В. For 1Q ~ N(95,10) : P(iq < 87.5) = ? Find the value w > 0 for which P(iq < 95 + w) = 0.8888 b. P(iq > 120) = ? a. с. C. For M - N(-5,2) :. Р(m <- 4) - ? P(-7 0) = ?

1. Recall that we write X ~ N(µ,0) for a random variable X whose values x follow a normal distribution with mean u and standard deviation ơ. Use a standard normal distribution table to find th following probabilities. Explain your answers, and illustrate each of your answers graphically: A. For Z - N(0,1) : P(z< 0.64) = ? P(- 1.32 < z< +1.32) = ? P(z> - 1.56) = ? P(0.59 < z<1.89) = ? b. d. В. For 1Q ~ N(95,10) : P(iq < 87.5) = ? Find the value w > 0 for which P(iq < 95 + w) = 0.8888 b. P(iq > 120) = ? a. с. C. For M - N(-5,2) :. Р(m <- 4) - ? P(-7 0) = ?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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1. Recall that we write X - N(u,0) for a random variable X whose values x follow a normal distribution with mean µ and standard deviation o. Use a standard normal distribution table to find the following probabilities. Explain your answers, and illustrate each of your answers graphically: A. For Z - N(0,1) : P(z < 0.64) = ? b. P(z>- 1.56) = ? P(0.59 <z< 1.89) = ? a. с. P(- 1.32 < z<+1.32)= ? d. В. For 10 ~ N(95,10) : P(iq < 87.5) = ? Find the value w > 0 for which P(iq < 95 + w) = 0.8888 а. b. P(iq > 120) = ? с. C. For M - N(-5,2) :. P(m <- 4) = ? P(-7<m<-3)= ? a. b. Р(m> 0) - ? 2. A Flemish student organisation claims that the average undergraduate student loan debt at a certain university in the capital Brussels is near to 12,500€. From previous analyses it is known that the standard deviation of the population of student loan debts is 1800€. The dean of the university doubts that the claim of the student organisation is correct. She thinks that in reality the average undergraduate student loan debt at their institution is less than 12500€, and decides to substantiate her suspicion via statistical hypothesis testing. As the level of significance for the test she chooses 5%. a. What will be the null hypothesis of the test? And what is the alternative hypothesis? The dean asks an assistant to send out an email questionnaire to a randomly chosen group of 31 undergraduate students. The received answers show an average debt of 11810€. b. Calculate the p-value for the sample. c. What will be the dean's conclusion? Why? d. Determine a 95% confidence interval for the average undergraduate student loan debt.
Transcribed Image Text:1. Recall that we write X - N(u,0) for a random variable X whose values x follow a normal distribution with mean µ and standard deviation o. Use a standard normal distribution table to find the following probabilities. Explain your answers, and illustrate each of your answers graphically: A. For Z - N(0,1) : P(z < 0.64) = ? b. P(z>- 1.56) = ? P(0.59 <z< 1.89) = ? a. с. P(- 1.32 < z<+1.32)= ? d. В. For 10 ~ N(95,10) : P(iq < 87.5) = ? Find the value w > 0 for which P(iq < 95 + w) = 0.8888 а. b. P(iq > 120) = ? с. C. For M - N(-5,2) :. P(m <- 4) = ? P(-7<m<-3)= ? a. b. Р(m> 0) - ? 2. A Flemish student organisation claims that the average undergraduate student loan debt at a certain university in the capital Brussels is near to 12,500€. From previous analyses it is known that the standard deviation of the population of student loan debts is 1800€. The dean of the university doubts that the claim of the student organisation is correct. She thinks that in reality the average undergraduate student loan debt at their institution is less than 12500€, and decides to substantiate her suspicion via statistical hypothesis testing. As the level of significance for the test she chooses 5%. a. What will be the null hypothesis of the test? And what is the alternative hypothesis? The dean asks an assistant to send out an email questionnaire to a randomly chosen group of 31 undergraduate students. The received answers show an average debt of 11810€. b. Calculate the p-value for the sample. c. What will be the dean's conclusion? Why? d. Determine a 95% confidence interval for the average undergraduate student loan debt.
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