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Question 1 (Normal Approximation). Suppose that 25% of Rackham graduate students are Graduate Student Instructor (GSI)....
H al Random Variable n=30 2. It has been reported that 39% of college students graduate...
H al Random Variable n=30 2. It has been reported that 39% of college students graduate in 4 years. Consider a random sample of thirty students, and let the random variable X be the number who graduate in 4 years. a. Find the probability that exactly 13 students in the sample of 30 graduate in 4 years. b. Find the probability that 15 or fewer students in the sample graduate in 4 years. That is, find PIX S15). c. Using...
1. In a particular facility, 60% of students are men and 40% are women. In a...
1. In a particular facility, 60% of students are men and 40% are women. In a random sample of 50 students what is the probability that more than half are women? Let the random variable X = number of women in the sample. Assume X has the binomial distribution with n = 50 and p = 0.4. What is the expected value and variance of the random variable X? (6 points) In a random sample of 50 students what is...
5. (20 pts) Suppose on a given college campus 45% of the students own an iPhone,...
5. (20 pts) Suppose on a given college campus 45% of the students own an iPhone, 50% an Android smartphone and 5% some other type of phone. Let X=the number of students in a simple random sample of 15 students who own an iPhone. A. What is the probability distribution of X? Note: If this is a well-known distribution it is sufficient to name the distribution and identify the value of the parameters B. Find the probability that 8 students...
Q4(3). Suppose the probability that a student finally goes to graduate school is 0.4. And there...
Q4(3). Suppose the probability that a student finally goes to graduate school is 0.4. And there are 100 student in the class AMS-102. Suppose the decision of one student will not affect the decision made by another student, which means students make their decisions independently. Please calculate (you do not need to give a concrete number. You only need to put the formula): (15 points, 3 for each) a) What is the appropriate random variable we could use to represent...
According to national data, about 13% of American college students earn a graduate degree. Using this estimate, what is...
According to national data, about 13% of American college students earn a graduate degree. Using this estimate, what is the probability that exactly 28 undergraduates in a random sample of 200 students will earn a college degree? Hint: Use the normal approximation to the binomial distribution, where p = 0.13 and q = 0.87. (Round your answer to four decimal places
sop Inta P. ssi *TV, Normal Approximation of Binomial. Cullege Graduate. About 34%ofworker, in the United...
sop Inta P. ssi *TV, Normal Approximation of Binomial. Cullege Graduate. About 34%ofworker, in the United States ase college graduates You domly molect 30 wockers and ask theun if they are a college graduate that it is appropiate to use a sormal distribution to approxiamste the binomial to use a A)tae a sample of n-so and p-34% to check B) ls a random ssmple of 50 workers, what is the probability that exactly 12 worlkers are college graduates? Write down...
11. A Biology instructor is wondering about the average amount of time a student spent studying...
11. A Biology instructor is wondering about the average amount of time a student spent studying for a test. She asks a random sample of 18 of her students for their amount of study time and determines that the mean study time in the sample is 6.3 hours with a standard deviation in the sample of 1.94 hours. She believes that it is reasonable to assume that the overall distribution of study times is normal. Give this instructor a 98%...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1),...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1), and Y-Σ-x. (a) Use CLT to get a large sample distribution of Y (b) For n 100, give an approximation for P(Y> 100) (c) Let X be the sample mean, then approximate P(.IX <1.2) for n 100. x, from CDF F(r)-1-1/z for 1 e li,00) and ,ero 2Consider a random sample Xi.x, 、 otherwise. (a) Find the limiting distribution of Xim the smallest order...
1. Suppose that random variables X and Y are independent and have the following properties: E(X)...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
11 0067 Normal approximation to Binomial Pages 299-305 a. School officials claim that about 13.5% (This...
11 0067 Normal approximation to Binomial Pages 299-305 a. School officials claim that about 13.5% (This is p) of the students who take out overnment backed loans to pay for college tuition default on their payments. What is the probability that a sample of 132 (this is n randomly selected students who have taken out government-backed loans will contain at most 111 students who will pay back their loan (ie, will not default)? Remember to use the correction for continuity....
H al Random Variable n=30 2. It has been reported that 39% of college students graduate in 4 years. Consider a random sample of thirty students, and let the random variable X be the number who graduate in 4 years. a. Find the probability that exactly 13 students in the sample of 30 graduate in 4 years. b. Find the probability that 15 or fewer students in the sample graduate in 4 years. That is, find PIX S15). c. Using...
5. (20 pts) Suppose on a given college campus 45% of the students own an iPhone, 50% an Android smartphone and 5% some other type of phone. Let X=the number of students in a simple random sample of 15 students who own an iPhone. A. What is the probability distribution of X? Note: If this is a well-known distribution it is sufficient to name the distribution and identify the value of the parameters B. Find the probability that 8 students...
Q4(3). Suppose the probability that a student finally goes to graduate school is 0.4. And there are 100 student in the class AMS-102. Suppose the decision of one student will not affect the decision made by another student, which means students make their decisions independently. Please calculate (you do not need to give a concrete number. You only need to put the formula): (15 points, 3 for each) a) What is the appropriate random variable we could use to represent...
sop Inta P. ssi *TV, Normal Approximation of Binomial. Cullege Graduate. About 34%ofworker, in the United States ase college graduates You domly molect 30 wockers and ask theun if they are a college graduate that it is appropiate to use a sormal distribution to approxiamste the binomial to use a A)tae a sample of n-so and p-34% to check B) ls a random ssmple of 50 workers, what is the probability that exactly 12 worlkers are college graduates? Write down...
11. A Biology instructor is wondering about the average amount of time a student spent studying for a test. She asks a random sample of 18 of her students for their amount of study time and determines that the mean study time in the sample is 6.3 hours with a standard deviation in the sample of 1.94 hours. She believes that it is reasonable to assume that the overall distribution of study times is normal. Give this instructor a 98%...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1), and Y-Σ-x. (a) Use CLT to get a large sample distribution of Y (b) For n 100, give an approximation for P(Y> 100) (c) Let X be the sample mean, then approximate P(.IX <1.2) for n 100. x, from CDF F(r)-1-1/z for 1 e li,00) and ,ero 2Consider a random sample Xi.x, 、 otherwise. (a) Find the limiting distribution of Xim the smallest order...
11 0067 Normal approximation to Binomial Pages 299-305 a. School officials claim that about 13.5% (This is p) of the students who take out overnment backed loans to pay for college tuition default on their payments. What is the probability that a sample of 132 (this is n randomly selected students who have taken out government-backed loans will contain at most 111 students who will pay back their loan (ie, will not default)? Remember to use the correction for continuity....
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