8. A group of 8 female managers and 17 male managers apply for a project. A random sample of 5 peopledrawn from a box (without replacement). What is the probability 4 of the chosen managers will befemale and 1 will be male? Also find the mean and variance of the hypergeometric distribution.

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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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Suppose a batch of steel rods produced at a steel plant have a mean length of 187 milimeters, and a Variance of 64. If 416 rods are sampled at random from the batch, what is the probability that the mean length all the sample rods would differ from the population mean by less than 0.65 millimeters? Round your answer to four decimal places.
Sketch the distribution, show the mean and standard error, and shade the part of the curve corresponding to your calculation. Suppose that at a large university, 34% of the students decide to take their classes online. 2. Now, if the researcher takes a different sample of 1000 students, what is the probability that at least 35% of the new sample will decide to take classes online?
Suppose babies born in a large hospital have a mean weight of 3685grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would be greater than 3631 grams? Round your answer to four decimal places.
About 79% of all female heart transplant patients will survive for at least 3 years. Eighty female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%? Assume the sampling distribution of sample proportions is a normal distribution. pq The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to n The probability that the sample proportion surviving for at least 3 years will be less than 70% is| (Round to four decimal places as needed.)
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8. An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. A Brother brand printer can print an average of 17.21 ppm and a standard deviation of 4 pages and its printer speed is also normally distributed. You select 10 of each printer at random. What is the probability that mean Brother print speed is at least 2 pages faster than the mean HP print speed?
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
About 71% of all female heart transplant patients will survive for at least 3 years. Eighty female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be pq less than 63%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to The probability that the sample proportion surviving for at least 3 years will be less than 63% is (Round to four decimal places as needed.) More Clear All Final Check Help Me Solve This View an Example Get More Help - 4:51 PM 73°F Rain coming 4* 10/4/2021 O Type here to search 10/05/17 EGO PrtSc Insert Delete 口回 F10 F11 F12 F7 F8 F9 F6 Esc F2 F4 F5 F1 F3 & Backspace Num Lock 5 6 2 R T. Y U Home G K L Enter F H. J + |I LEGY P * 00 44 %#3 山

4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
Suppose the horses in a large stable have a mean weight of 873lbs, and variance of 17,161. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 50 horses are sampled at random from the stable? Round your answer to four decimal places.
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Suppose the ages of Internet shoppers have a mean of 32 years and a standard deviation of 5 years. If you select a random sample of 100 Internet shoppers, what is the probability that the average age of the sample is 30.9 years or more? (use the concept of sampling distribution of mean and central limit theorem)

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8. A group of 8 female managers and 17 male managers apply for a project. A random sample of 5 people drawn from a box (without replacement). What is the probability 4 of the chosen managers will be female and 1 will be male? Also find the mean and variance of the hypergeometric distribution.