finalS03_answer

finalS03_answer - Economics 120A July 30, 2003 Name: _key_...

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Economics 120A Name: ________key_________________ July 30, 2003 Student ID#: _________________________ ANSWER to Final Exam: Econometrics 1.(10 points) The stamping machine on a production line periodically is taken off-line for maintenance. Assume that the amount of time the machine is off-line is uniformly distributed between 15 and 30 minutes. What is the probability that the machine is off- line for more than 18 minutes? What is the probability that the machine is off-line between 21 and 27 minutes? (Answer) (a) 18 to 30 minutes represent 80% of the distance between 15 and 30 minutes. (b) The range 21 to 27 is 40% of the distance between 15 and 30 minutes. 2. (10 points) The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 minutes and a standard deviation of 1.3 minutes. If the sandwich shop employees make $6.00 an hour, what is the mean and standard deviation for the labor costs per sandwich? (answer) E(X) = 4.1 sd(X) = 1.3 Labor cost per minute = $0.10 Y = 0.10X E(Y) = (0.10)(4.1) = $0.41 sd(Y) = 0.1*sd(X) = 0.13.
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FINAL EXAM, ECON 120A, SUMMER 2003 3. (15 points) Let the random variable Z follow a standard normal distribution. Calculate the following probabilities. What is the probability P(Z>0.29)? Note F(0.29)=0.6141. What is the probability P(-0.44<Z<1.2)? Note F(0.44)=0.6700 and Note F(1.2)=0.8849. (Answer) (a.) P(Z>0.29) = 1-F(0.29)=1-0.6141=0.3859. (b) P(-0.44<Z<1.2)= F(1.2)-F(-0.44)= F(1.2)-(1-F(0.44))= 0.8849-(1-0.6700)= 0.5549. 4. (15 points) Let the random variable Z follow a standard normal distribution. Calculate the following values. Show the calculation procedure. Find the value k, such that P(Z>k) = 0.43. Note F(0.17)=0.57 Find the value k, such that P(-0.71<Z<k) = 0.67. Note F(0.71)=0.7611, F(1.33)=0.9089 (Answer) (a) P(Z>k) =0.43, P(Z k) =0.57. Since F(0.17)=0.57, so k=0.17 (b) P(-0.71<Z<k)=0.67, F(k)-F(-0.71)=0.67, Note that F(0.71)=0.7611. F(-0.71)=1-F(0.71)=0.2389. F(k)=F(-0.71)+0.67=0.9089. Note that
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This note was uploaded on 04/15/2008 for the course ECON 120A taught by Professor Jeyeon during the Summer '08 term at UCSD.

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finalS03_answer - Economics 120A July 30, 2003 Name: _key_...

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