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exercise05

# exercise05 - = r pq n = r 88 12 80 = 03633180 np =(80 88 =...

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Econ 41 Statistics for Economists Summer 2007 Chunming Yuan EXERCISES FROM TEXTBOOK Chapter 7: 7.94 7.96 7.99 7.109

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7.94 μ =24 minutes, σ =7 minutes, and n = 100 μ x = μ =24 minutes and σ x = σ n = 7 100 = . 7 minutes The sampling distribution of x is approximately normal because n > 30 7.96 μ =24 minutes, σ =7 minutes, and n = 100 μ x = μ =24 minutes and σ x = σ n = 7 100 = . 7 minutes a. For x =22: z = ( x μ ) σ x = (22 24) . 7 = 2 . 86 P ( x< 22) = P ( z< 2 . 86) = . 0021 b. For x =23: z = ( x μ ) σ x = (23 24) . 7 = 1 . 43 For x =26: z = ( x μ ) σ x = (26 24) . 7 =2 . 86 P (23 < x< 26) = P ( 1 . 43 <z< 2 . 86) = P ( z< 2 . 86) P ( z< 1 . 43) = . 9979 . 0764 = . 9215 c. P ( x within 1 minute of μ )= P (23 x 25) For x =23: z = ( x μ ) σ x = (23 24) . 7 = 1 . 43 For x =25: z = ( x μ ) σ x = (25 24) . 7 =1 . 43 P (23 x 25) = P ( 1 . 43 z 1 . 43) = P ( z 1 . 43) P ( z ≤− 1 . 43) = . 9236 . 0764 = . 8472 d. P ( x greater than μ by 2 minutes or more )= P ( x 26) For x =26: z = ( x μ ) σ x = (26 24) . 7 =2 . 86 1
P ( x 26) = P ( z 2 . 86) = 1 P ( z 2 . 86) = 1 . 99979 = . 0021 7.99 p = . 88 ,q =1 p =1 . 88 = . 12 , and n =80 μ e p = p = . 88 , and σ e p =
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Unformatted text preview: = r pq n = r ( . 88)( . 12) 80 = . 03633180 np = (80) ( . 88) = 70 . 4 > 5 , nq = (80)( . 12) = 9 . 6 > 5 Since np and nq are both greater thatn 5, the sampling distribution of b p is approximately normal. 7.109 μ = 160 pounds, σ = 25 pounds, and n = 35 μ x = μ = 160 pounds and σ x = σ √ n = 25 √ 35 = 4 . 22577127 pounds Since n > 30 , x is approximately normally distributed. P ( sum of 35 weights exceeds 6000 pounds ) = P ( mean weight exceeds 6000/35 ) = P ( x > 171 . 43) For x = 171 . 43 : z = ( x − μ ) σ x = (171 . 43 − 160) 4 . 22577127 = 2 . 70 P ( x > 171 . 43) = P ( z > 2 . 70) = 1 − P ( z ≤ 2 . 70) = 1 − . 9965 = . 0035 2...
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exercise05 - = r pq n = r 88 12 80 = 03633180 np =(80 88 =...

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