Jiao works as an usher at a theater. The theater has 100010001000 seats that are accessed through five entrances. Each guest should use the entrance that's marked on their ticket. Jiao wants to test if the distribution of guests according to entrances matches the official distribution. He collects information about the number of guests that went through each entrance at a certain night. Here are the results:
Entrance \text AAstart text, A, end text \text BBstart text, B, end text \text CCstart text, C, end text \text DDstart text, D, end text \text EEstart text, E, end text Total
Expected 30\%30%30, percent 30\%30%30, percent 20\%20%20, percent 10\%10%10, percent 10\%10%10, percent 100\%100%100, percent
# of people 398398398 202202202 205205205 878787 108108108 100010001000
Jiao wants to perform a \chi^2χ
2
\chi, squared goodness-of-fit test to determine if these results suggest that the actual distribution of people doesn't match the expected distribution.
What is the expected count of guests in entrance \text AAstart text, A, end text in Jiao's sample?
You may round your answer to the nearest hundredth.
Expected: