In amusement park considering adding some new attractions,conducted a study over several typical days and found that ,of 10,000 families entering the park ,1024 brought just one child (define as younger than age 12),3370 brought two children ,3510 brought three children,1340 brought four children,510 brought five children,80 brought six children and 170 brought no children at all . Find the expected number of children per family attending this park

please show me the work
Answer is 2.7

expectations

= 1(1024/10000) + 2(3370/10000) + 3(3510/10000) + 4(1340/10000)+ 5(510/10000) + 80(6/10000) + 0(170/10000)
= 1/10000 (1024 + 6740 + 10530 +5720 + 2700 + 480 + 0)
=27194/10000 = appr 2.7

To find the expected number of children per family attending the park, you need to calculate the weighted average of the number of children in each family.

First, let's calculate the total number of families:
Total families = Number of families with 1 child + Number of families with 2 children + Number of families with 3 children + Number of families with 4 children + Number of families with 5 children + Number of families with 6 children + Number of families with no children
Total families = 1024 + 3370 + 3510 + 1340 + 510 + 80 + 170 = 10,004

Next, determine the total number of children:
Total children = (Number of families with 1 child x 1) + (Number of families with 2 children x 2) + (Number of families with 3 children x 3) + (Number of families with 4 children x 4) + (Number of families with 5 children x 5) + (Number of families with 6 children x 6)
Total children = (1024 x 1) + (3370 x 2) + (3510 x 3) + (1340 x 4) + (510 x 5) + (80 x 6) = 28,770

Finally, calculate the expected number of children per family by dividing the total number of children by the total number of families:
Expected number of children per family = Total children / Total families
Expected number of children per family = 28,770 / 10,004
Expected number of children per family ≈ 2.879

Rounded to one decimal place, the expected number of children per family attending the park is approximately 2.7.