Nora Bakery would like to determine how many birthday cakes to bake at the beginning of each day in order to lnaxil'nize the daily expected prot. Each birthday cake costs the bakery $10 and it can be sold for $35 each. However, all leftover birthday cakes at the end of each day will be donated to nonprot organizations. Due to the manpower restriction, the bakery can only bake no more than ve cakes in one day. Statistical analysis has shown that the daily demand of cakes is a random variable with the following probability mass function: Demand of Cakes | 2 Probability (L25 Let X be net prot per day if five birtl'lday cakes are baked in ear-.11 day. a) Find the probability mass function of X. ( (1)) Find the cumulative distribution [innitim'l of X. (1') Find the mean and standard deviation of X. ( (1] 'Will the expected prot, be. higher if only [our birthday cakes are baked in ear-ll day? Justify your