Question 1158362
53%+29%+18%=100%, so the portion of people who check more than two bags must have been indeed negligible.
The passenger who check two bags pay $25+$30=$55
 
a) The average baggage-related revenue per passenger (rounded to the nearest cent):
The fractions of people who check 0, 1, and 2 bags are 0.53, 0.29, and 0.18 respectively, and add to 1.00,
so the averaged revenue per passenger is the weighted average
{{{0.53*"$0"+0.29*"$25"+0.18*"$55"="$0"+"$7.25"+0.18*"$9.9"=highlight("$17.15")}}}
 
b) The standard deviation of baggage-related revenue (per passenger, in $, rounded to the nearest cent):
The standard deviation (in $) of baggage-related revenue  per passenger can be calculated from the individuals deviations (in $) from the average:
{{{0-17.15=-17.15}}}  for 53% of the passengers,
{{{25-17.15=7.85}}} for 29%, and
{{{55-17.15=37.85}}} for 18% of the passengers.
{{{sigma=sqrt(0.53*(-17.15)^2+0.29*7.85^2+0.18*37.85^2)= sqrt(0.53*294.1225+0.29*61.6225+0.18*1432.6225)=sqrt(155.884925+17.870525+257.87205)=sqrt(431.6275)=highlight(20.78)}}}(in $, rounded to the nearest cent)
 
c) Revenue the airline should expect for a flight of 130 passengers (in $, rounded to the nearest dollar)
{{{130*17.15=2229.50=highlight(2230)}}}(in $, rounded to whole dollars).