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chpt5ReviewProblems1 - Review Exercises I 7 I when the...

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Unformatted text preview: Review Exercises I 7 I when the expected number of successes (or failures) is too small. That is, when either np or n(1 —p)is 15 orless 2. Don’t add variances according to Var(X1+ X2) = Var(X1)+ Var(X2) unless the two random variables are independent or have zero covariance. 3. Don’t just assume that data come from a normal distribution. When there are at least 20 to 25 observations, it is good practice to construct a normal scores plot to check this assumption. ‘09 If the probability density of a random variable is pt 2 4.76 seconds and a = 0.04 second. What is the given by . , probability that this kind of rocket will burn 1 th 4.66 d ; k(1—x2) for0<x<l (a) ess an secons f (x) = 0 1 h (b) more than 4.80 seconds; e sew ere (c) anywhere from 4.70 to 4.82 seconds? find the value of k and the probabilities that a random 5.115 Verify that 12$th havrng this probability denSity Will take on a (a) 10.10 = 1.28; () betw 01 d 0 2- (b) mom = 3'09' J a een ' an i ’ 5.116 Referring to Exercise 5.28, find the quaniles of the 01) greater than 0-5- normal distribution with n = 102 and o = 27. 10 Withreference to the preceding exercise. find the corre— 5.117 The probability density shown in Figure 5.20 is the spending distribution function and use it to determine log-normal distribution with a = 8.85 and ,3 = 1.03 the probabilities that a random variable having this dis- Find the probability that mum“ fimcmn “”11”“ ”“311” (a) the interrequest time is more than 200 micro— (a) less than 0.3; seconds; (b) between 0.4 and 0.6- (b) the interrequest time is less than 300 micro— 1 In certain experiments, the error made in determining seconds. the density of a silicon compound is a random variable 5.118 The probability density shown in Figure 5.22 is the having the probability density exponential distribution 25 for — 0.02 < x < 0.02 0.25 [0.25. 0 < x f(x) = { 0 elsewhere f(x) = {0 elsewhere Find the probabilities that such an error will be (a) between —0.03 and 0.04; Find the probability that (a) the time to observe a particle is more than (b) between —0.005 and 0.005. 200 microseconds; 12 Find p. and 02 for the probability density of Exer— (b) the time to observe a particle is less than cise 5.109. 10 microseconds. '43 If a random variable has the standard normal distribu- 5.119 Referring to the normal scores in Exercise 5.101, con— tiOIl. find the probability that it will take on a value struct a normal scores plot of the suspended solids data (a) between 0 and 250; in Exerc1se 2.68. (b) between 1.22 and 235; 5.120 Referring to the normal scores in Exercise 5.101, con- struct a normal scores plot of the velocity of light data (0) between ‘1-33 and ‘0-33; in Exercise 2.66. (d) between _1'60 and 1'80' 5121 If n salespeople are employed in a door-to-door sell- " 4 The burning time of an experimental rocket is a ing campaign, the gross sales volume in thousands of random variable having the normal distribution with dollars may be regarded as a random variable having 1 ...
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