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5.120. Calculate the first four moments about the mean for the distribution of Table 5-22.

CHAP. 15]

Table 5-22

RLOSS(R) 100 500

5.121. Calculate the first four moments about the mean for the distribution of Problem 5.97. 5.122. Find (a) m1, (b) m2, (c) m3, (d) m4, (e) x, (f) s, (g) x2 (h) x3, (i) x4, (j) (x # Problem 5.100. 1)3 for the distribution of

Estimated E ort (programmerdays) 30 25 30 50 60 35 55 30 45 25 45 Actual E ort (programmerdays) 37 24 41 47 63 31 58 28 43 29 49

5.123. Find the coefficient of (a) skewness, (b) kurtosis for the distribution Problem 5.120. 5.124. Find the coefficient of (a) skewness, (b) kurtosis for the distribution of Problem 5.97. See Problem 5.121. 5.125. The second moments about the mean of two distributions are 9 and 16, while the third moments about the mean are 8.1 and 12.8, respectively. Which distribution is more skewed to the left 5.126. The fourth moments about the mean of the two distributions of Problem 5.125 are 230 and 780, respectively. Which distribution more nearly approximates the normal distribution from the viewpoint of (a) peakedness, (b) skewness

2 10 3000

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5127 A population of 7 numbers has a mean of 40 and a standard deviation of 3 If samples of size 5 are drawn from this population and the variance of each sample is computed, find the mean of the sampling distribution of variances if sampling is (a) with replacement, (b) without replacement 5128 Certain tubes produced by a company have a mean lifetime of 900 hours and a standard deviation of 80 hours The company sends out 1000 lots of 100 tubes each In how many lots can we expect (a) the mean lifetimes to exceed 910 hours, (b) the standard deviations of the lifetimes to exceed 95 hours What assumptions must be made 5129 In Problem 5128 if the median lifetime is 900 hours, in how many lots can we expect the median lifetimes to exceed 910 hours Compare your answer with Problem 5.

The resonance curves are shown with greater detail in Fig. 15-29(b).

128(a) and explain the results 5130 On a citywide examination the grades were normally distributed with mean 72 and standard deviation 8 (a) Find the minimum grade of the top 20% of the students (b) Find the probability that in a random sample of 100 students, the minimum grade of the top 20% will be less than 76 5131 (a) Prove that the variance of the set of n numbers a, a d, a 2d, c, a (n 1) d (ie, an arithmetic 1 progression with first term a and common difference d) is given by 12(n2 1)d2 [Hint: Use 1 2 c (n 1) 1 n(n 1), 12 22 32 c (n 1)2 1 n (n 1)(2n 3 1)] 2 6 (b) Use (a) in Problem 5103 5132.

Prove that the first four moments about the mean of the arithmetic progression a, a a (n 1)d are m1 0, m2 1 2 (n 12 1)d2, 24 m3 34 0, c m4 (n 1 (n2 240 1)4.

Fig. 15-29

2d, c,

Estimated Completion Date 1/1 2/15 3/1 4/15 5/1 5/15 6/1 6/15 7/1 8/1 8/15

Use .TRAN and .PROBE to plot VC across the 1-mF capacitor in the source-free circuit of Fig. 15-30(a) for R 100, 600, 1100, 1600, and 2100

7)d4 1)(3n2 3n 1) .]

Compare with Problem 5.114. [Hint: 14

Natural response of RC, Fig. 15-30(a) R 0 1 Rshunt C 1 0 1 uF .MODEL Rshunt RES R 1 .STEP LIN RES .TRAN 1E 4 50E 4 .PLOT TRAN V(1) .PROBE .END

5.49. (a) 9.0 (b) 4.47 (c) 9.0 (d) 3.16 5.51. (a) mX 5.52. (a) mX 22.40 oz, sX 22.40 oz, sX 5.50. (a) 9.0 (b) 4.47 (c) 9.0 (d) 2.58 22.40 oz, sX is slightly less than 0.008 oz 22.40 oz, sX 0.0057 oz

The graph of the voltage VC is shown in Fig. 15-30(b).

5.53. (a) 237 (b) 2 (c) none (d) 24

5.54. (a) 0.4972 (b) 0.1587 (c) 0.0918 (d) 0.9544 5.56. 0.0026

Fig. 15-30

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