Why are these two questions solved differently? 3. Flo-Anna’s diner in Shoreline

Question

Why are these two questions solved differently?

3. Flo-Anna’s diner in Shoreline does an average of $16,000 in net sales per month, with a standard deviation of $3,000. Last month, Flo-Anna’s diner made $5,000 in net sales. a. Calculate the z-score and estimate the probability of having a monthly net sale of $5,000.

z = (5000 – 16000) / 3000 = –3.67; P < 0.0002 since the table you have only goes to –3.49. b. Is this an unusual occurrence for Flo-Anna? Explain. Yes, because the probability of a monthly sale as low as $5,000 is less than 0.0002, or less than 0.02%, which is far less than 5%

4. Since opening her diner in 1993, Flo-Anna’s has done an overall average of $16,000 in net sales per month, with a standard deviation of $3,000. a. In 2015, Flo-Anna averaged $13,500 per month in net sales. Calculate the z-score from the mean net sales from 2015 and estimate the probability associated with this new mean. Is this an unusual occurrence for Flo-Anna? Explain.

First, calculate the standard error of the mean for the 12 months in 2015: = = 3000 12 = 866.03 = 13500 16000 866.03 = 2.89 Look up z-score of –2.89 on the standard Normal table, the probability is 0.0019. Yes, this is unusual because it is far less than 5%.

Explanation / Answer

the question number asked about monthly sale while question number 4 asked about mean (or average) monthly sale. In question number no need to apply central limit theorem while in question 4 central limit theorem is applied for sample size n=12.

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