Quiz4 - Please derive the general formula first. Solution:...

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AMS312.01 Quiz 4 Spring 2010 ♠♣♥♦ Name: ________________________________ ID: ____________________ Signature: ________________________ Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. The exam goes from 1:00-1:30pm. Good luck! Jerry is planning to purchase a sporting goods store. He calculated that in order to cover basic expenses average daily sales must be at least $525. He checked the daily sales of 36 randomly selected business days. And he found that the average daily sale for these days is $565 with a standard deviation of $150. In order to estimate the average daily sale of the store to within $20 with 95% reliability, how many days should Jerry sample?
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Unformatted text preview: Please derive the general formula first. Solution: First we derive the general formula. ( ) 1 ( ) 1 ( ) 1 / / / P X E P E X E E X E P n n n - = --- = --- = -By the central limit theorem, when the sample size is large, 2 / 2 / 2 (0,1) / / z X E Z N z n E n n- = : & When is unknown, we can estimate its value using the sample standard deviation, here being s = 150 Now we plug in the values to obtain the answer for the given problem: 2 2 / 2 1.96*150 216.09 217 20 z n E . Therefore a total of 217 days must be sampled....
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This note was uploaded on 11/14/2010 for the course AMS 312 taught by Professor Zhu,w during the Spring '08 term at SUNY Stony Brook.

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