A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 20% of potential customers will choose the Day Plan, which does not include overnight accommodations; 40% will choose the Overnight Plan, which includes one night at the resort; and 40% will choose the Weekend Plan, which includes two nights.
a) Find the expected value of the number of nights potential customers will need.
b) Find the standard deviation of the number of nights potential customers will need.