4. You are interested in purchasing a local store whose ownerclaims that average

Question

4. You are interested in purchasing a local store whose ownerclaims that average daily sales is over $850 per day 75% of thetime. Suppose you intend to monitor the business receipts for thenext 20 days.
   a. Estimate theprobability the store will have sales at least 7 out of the 20days.    b. Fewer than 7days.    c. Between 10 and 15days?    d. What is theexpected number of days the store will have sales of $850 ormore?    e. Could normalmethods be used to evaluate this problem? Explain. 4. You are interested in purchasing a local store whose ownerclaims that average daily sales is over $850 per day 75% of thetime. Suppose you intend to monitor the business receipts for thenext 20 days.
   a. Estimate theprobability the store will have sales at least 7 out of the 20days.    b. Fewer than 7days.    c. Between 10 and 15days?    d. What is theexpected number of days the store will have sales of $850 ormore?    e. Could normalmethods be used to evaluate this problem? Explain.

Explanation / Answer

First, use binomcdf to find the "at least 7" probability We find "6 or fewer" probability and do 1- that value to findthe prob. of "7 or more" Part a) 1-binomcdf(20,.75,6)=.99997, or about 99.997% Part b) binomcdf(20,.75,6)=.000029512, or about .00295% Part c) prob. of 9 or less: binomcdf(20,.75,9)=.00394 (not 10or less b/c we will be subtracting later)             prob.of 15 or less: binomcfd(20,.75,15)=.585158    subtract these two:.5851580-.00394=.5812159, or baout 58.12% The expected value is just .75*20, or 15days. e) Normal methods should NOT be used to evaluate theseproblems because the sample size is less than 30, which means thenormal approximation to the binomial distribution is not accurateenough. e) Normal methods should NOT be used to evaluate theseproblems because the sample size is less than 30, which means thenormal approximation to the binomial distribution is not accurateenough.

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