# ssrs export to pdf barcode font Sampling distributions of differences and sums in Software Draw QR-Code in Software Sampling distributions of differences and sums

Sampling distributions of differences and sums
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5.63. A and B manufacture two types of cables, having mean breaking strengths of 4000 and 4500 lb and standard deviations of 300 and 200 lb, respectively. If 100 cables of brand A and 50 cables of brand B are tested, what is the probability that the mean breaking strength of B will be (a) at least 600 lb more than A, (b) at least 450 lb more than A 5.64. What are the probabilities in Problem 5.63 if 100 cables of both brands are tested Account for the differences. 5.65. The mean score of students on an aptitude test is 72 points with a standard deviation of 8 points. What is the probability that two groups of students, consisting of 28 and 36 students, respectively, will differ in their mean scores by (a) 3 or more points, (b) 6 or more points, (c) between 2 and 5 points 5.66. An urn holds 60 red marbles and 40 white marbles. Two sets of 30 marbles each are drawn with replacement from the urn, and their colors are noted. What is the probability that the two sets differ by 8 or more red marbles 5.67. Solve Problem 5.66 if sampling is without replacement in obtaining each set. 5.68. The election returns showed that a certain candidate received 65% of the votes. Find the probability that two random samples, each consisting of 200 voters, indicated a greater than 10% difference in the proportions that voted for the candidate. 5.69. If U1 and U2 are the sets of numbers in Problem 5.12, verify that (a) mU1 (b) sU1 U2 !s2 1 s2 2 . U U mU1 mU2,
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5.70. Three weights are measured as 20.48, 35.97, and 62.34 lb with standard deviations of 0.21, 0.46, and 0.54 1b, respectively. Find the (a) mean, (b) standard deviation of the sum of the weights. 5.71. The voltage of a battery is very nearly normal with mean 15.0 volts and standard deviation 0.2 volts. What is the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts
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Sampling distribution of variances
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5.72. With reference to Problem 5.49, find (a) the mean of the sampling distribution of variances, (b) the standard error of variances. 5.73. Work Problem 5.72 if sampling is without replacement.
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CHAPTER 5 Sampling Theory
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5.74. A normal population has a variance of 15. If samples of size 5 are drawn from this population, what percentage can be expected to have variances (a) less than 10, (b) more than 20, (c) between 5 and 10 5.75. It is found that the lifetimes of television tubes manufactured by a company have a normal distribution with a mean of 2000 hours and a standard deviation of 60 hours. If 10 tubes are selected at random, find the probability that the sample standard deviation will (a) not exceed 50 hours, (b) lie between 50 and 70 hours.
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Case where population variance is unknown
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5.76. According to the table of Student s t distribution for 1 degree of freedom (Appendix D), we have P( 1 T 1) 0.50. Check whether the results of Problem 5.1 are confirmed by this value, and explain any difference. 5.77. Check whether the results of Problem 5.49 are confirmed by using (a) P( 1 T (b) P( 1.376 T 1.376) 0.60, where T has Student s t distribution with n 1) 1. 0.50,
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5.78. Explain how you could use Theorem 5-7, page 159, to design a table of Student s t distribution such as that in Appendix D.
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Sampling distribution of ratios of variances
5.79. Two samples of sizes 4 and 8 are drawn from a normally distributed population. Is the probability that one variance is greater than 1.5 times the other greater than 0.05, between 0.05 and 0.01, or less than 0.01 5.80. Two companies, A and B, manufacture light bulbs. The lifetimes of both are normally distributed. Those for A have a standard deviation of 40 hours while the lifetimes for B have a standard deviation of 50 hours. A sample of 8 bulbs is taken from A and 16 bulbs from B. Determine the probability that the variance of the first sample is more than (a) twice, (b) 1.2 times, that of the second. 5.81. Work Problem 5.80 if the standard deviations of lifetimes are (a) both 40 hours, (b) both 50 hours.