please answer all parts to question 3.132 and show a step by step to how you get

Question

please answer all parts to question 3.132 and show a step by step to how you get there

Applying the Concepts and Skils Applying the Concepts and Skills 3.132 Exam Scores. Comsider the following sample ofexam scores. arranged in increasing order. 28 57 58 64 69 74 79 80 83 85 85 87 87 89 89 90 92 93 94 94 95 96 96 97 97 97 97 98 100 100 The sample mean and sample standard deviation of these exam scores are 85 and 16.1, respectively. Modeling your solutions after those in Example 3.15 on pages 117-118, solve the following problems, a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule with k = 2. b. Repeat part (a) with k = 3. c. Interpret your results from parts (a) and (b).

Explanation / Answer

mean=85 and sample stanard deviation =s=16.1

mean+2s=85+2*16.1=117.2

mean+2s=85-2*16.1=52.8

out of 30 there are 29 observation comes under the range of (52.8,117.2)

so 29/30=0.9667 =96.67% observation comes under two standerad deviation from either side of the mean..

According to chebyshev's rule

P(|x-mean|/s<k)>1-1/k2

for k=2, so P(|x-mean|/s<2)>1-1/(2*2)=0.75

so observation comes under two standerad deviation from either side of the mean is more than 75%

(b) for k=3, P(|x-mean|/s<3)>1-1/(3*3))=0.89

so observation comes under two standerad deviation from either side of the mean is more than 89%

(c) so larger the value of k, wider the range...

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