A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 40% 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 20% will choose the Weekend Plan, which includes two nights.

Complete parts a and b below.

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.