Answer to Question #113215 in Statistics and Probability for ralph

Question

4. To determine the average amount of purchases of its customers, a convenience store samples 150 of its customers. The average purchase of the group is Php 125. If the store knew that the standard deviation of all purchase is Php 50, what is the 95% confidence interval for the average purchase in the store?

Answer 1

$\text{The confidence interval for the mean }\\ \text{can be calculated as follows:}\\ \bar x±Z_{\frac{α}{2}}(\frac{s}{\sqrt{n}}),\\ \bar x=125\\ Z_{\frac{α}{2}}=Z_{\frac{0.05}{2}}=Z_{0.025}=1.96,\\ s=50\\n=150\\ \text{ the lower limit }= 125-1.96(\frac{50}{\sqrt{150}})\\ ≈116.998,\\ \text{ the upper limit} = 125+1.96(\frac{50}{\sqrt{150}})\\ ≈133.002,\\ \text{so the confidence interval is}\\ 116.998\leq \bar x \leq 133.002\\$