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 05 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 lognormal 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 ‘133 and ‘033; in Exercise 2.66. (d) between _1'60 and 1'80' 5121 If n salespeople are employed in a doortodoor 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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 Fall '08
 Mendell

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