Answer to Question #268391 in Statistics and Probability for Spong

Question

Engr. Joey Mutia, the marketing director of a large department store, wants to estimate the average number of customers who enter the store every 5 minutes. He randomly selects 5-minute intervals and counts the number of arrivals at the store. She obtains the figures 58, 32, 41, 47, 56, 80, 45, 29, 32, and 78. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all 5-minute intervals. What interval values would Engr. Mutia get to estimate the average number of customers per 5 minutes?

Answer 1

$\overline{x}=\sum x_i/n=49.8$

$\sigma=\sqrt{\sum(x_i-\overline{x})^2/(n-1)}=18.22$

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt n}=\frac{49.8-\mu}{18.22/\sqrt{10}}$

critical values for 95% confidence interval:

$Z_{0.95}=\pm 1.96$

then:

$-1.96<\frac{49.8-\mu}{18.22/\sqrt{10}}<1.96$

$-11.3<49.8-\mu<11.3$

$38.5<\mu<61.1$