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the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Find the probability of a pregnancy lasting more then 250 Days. (b) Find the Probabilty of a pregnancy lasting more than 280 days. these two problems can be solved by the same procedure.draw the diagram for each and discuss he difference. then, explain why the same procedure can be used.

the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Find the probability of a pregnancy lasting more then 250 Days. (b) Find the Probabilty of a pregnancy lasting more than 280 days. these two problems can be solved by the same procedure.draw the diagram for each and discuss he difference. then, explain why the same procedure can be used.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Find the probability of a pregnancy lasting more then 250 Days. (b) Find the Probabilty of a pregnancy lasting more than 280 days. these two problems can be solved by the same procedure.draw the diagram for each and discuss he difference. then, explain why the same procedure can be used.

中国移动令 2:04 PM © 66% MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following best describes the expected value of a discrete random variable? A). It is the middle value of all possible outcomes B). It is the weighted average over all possible outcomes. C). It is the simple average over all possible outcomes D). None of the above 2) A 28-year-old man pays $158 for a one-year life insurance policy with coverage of $110,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? A) $66.00 B) -$92.00 C) $109,934.00 3) A company manufactures batteries in batches of 8 and there is a 3% rate of defects. Find the D) -$157.91 mean number of defects per batch. A) 0.232 B) 0.248 C) 0.24 D) 7.76 4) In a certain town, 50% of voters favor a given ballot measure. For groups of 22 voters, find the variance for the number who favor the measure. A) 2.35 B) 5.50 C) 11.00 D) 30.25 5) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week? A) 0.2823 B) 0.1003 C) 0.7823 D) 0.2177 6) A final exam in Calculus has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70. A) 0.1.006 B) 0.0301 C)0.9699 D) 0.0278 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1. Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Find the probability of a pregnancy lasting more than 250 days. (b) Find the probability of a pregnancy lasting more than 280 days. These two problems can be solved by the same procedure. Draw the diagram for each and discuss the difference. Then, explain why the same procedure can be used. 2. Find the mean and variance of the r.v. X if it has p.m.f. P(X = 1) = 0.2, P(X = 2) = 0.3 and P(X = 3) = 0.5. 3. In a large class, on exam 1, the mean and standard deviation of scores were 78 and 20, respectively. For exam 2, the mean and standard deviation were 72 and 15, respectively. The covariance of the exam scores was 80. Give the mean and standard deviation of the sum of the two exam scores. Assume all students took both exams. 4. A continuous r.v. (X,Y) with joint pdf 0<x< 2,0<y<2 otherwise Find the correlation coefficient Py.
Transcribed Image Text:中国移动令 2:04 PM © 66% MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following best describes the expected value of a discrete random variable? A). It is the middle value of all possible outcomes B). It is the weighted average over all possible outcomes. C). It is the simple average over all possible outcomes D). None of the above 2) A 28-year-old man pays $158 for a one-year life insurance policy with coverage of $110,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? A) $66.00 B) -$92.00 C) $109,934.00 3) A company manufactures batteries in batches of 8 and there is a 3% rate of defects. Find the D) -$157.91 mean number of defects per batch. A) 0.232 B) 0.248 C) 0.24 D) 7.76 4) In a certain town, 50% of voters favor a given ballot measure. For groups of 22 voters, find the variance for the number who favor the measure. A) 2.35 B) 5.50 C) 11.00 D) 30.25 5) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week? A) 0.2823 B) 0.1003 C) 0.7823 D) 0.2177 6) A final exam in Calculus has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70. A) 0.1.006 B) 0.0301 C)0.9699 D) 0.0278 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1. Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. (a) Find the probability of a pregnancy lasting more than 250 days. (b) Find the probability of a pregnancy lasting more than 280 days. These two problems can be solved by the same procedure. Draw the diagram for each and discuss the difference. Then, explain why the same procedure can be used. 2. Find the mean and variance of the r.v. X if it has p.m.f. P(X = 1) = 0.2, P(X = 2) = 0.3 and P(X = 3) = 0.5. 3. In a large class, on exam 1, the mean and standard deviation of scores were 78 and 20, respectively. For exam 2, the mean and standard deviation were 72 and 15, respectively. The covariance of the exam scores was 80. Give the mean and standard deviation of the sum of the two exam scores. Assume all students took both exams. 4. A continuous r.v. (X,Y) with joint pdf 0<x< 2,0<y<2 otherwise Find the correlation coefficient Py.
l 中国移动令 2:04 PM @ 66% 1/1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the Central Limit theorem apply for this problem? True or False The Central Limit Theorem states that as we increase our sample size towards infinity, the distribution of sampled measurements tends to be approximately normal, regardless of the shape of the population of individual measurements. Based on the Central Limit Theorem:. 1) Give the approximate sampling distribution for the following quantity based on random samples of independent observations: X + .. + X00 where E(X) = 100 V(x) = 400 100 2) What is the approximate probability the sample mean will be between 96 and 104? The daily number of arrivals to a rural emergency room is a Poisson random variable with a mean of 100 people per day. Use the normal approximation to the Poisson distribution to obtain the approximate probability that 112 or more people arrive in a day.
Transcribed Image Text:l 中国移动令 2:04 PM @ 66% 1/1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the Central Limit theorem apply for this problem? True or False The Central Limit Theorem states that as we increase our sample size towards infinity, the distribution of sampled measurements tends to be approximately normal, regardless of the shape of the population of individual measurements. Based on the Central Limit Theorem:. 1) Give the approximate sampling distribution for the following quantity based on random samples of independent observations: X + .. + X00 where E(X) = 100 V(x) = 400 100 2) What is the approximate probability the sample mean will be between 96 and 104? The daily number of arrivals to a rural emergency room is a Poisson random variable with a mean of 100 people per day. Use the normal approximation to the Poisson distribution to obtain the approximate probability that 112 or more people arrive in a day.
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