Question

20. The owner of a doughnut shop knows from past experience that on a daily basis, 80% of the apple fritters made are sold. Based on this knowledge, the owner makes 30 fritters available for sale on a given day (a) If the owner needs to sell 20 fritters a day to break even find the probability that on a given day she will make a profit (b) What is the probability that, over a 7 day period, the owner will make a profit on at least six days. (Hint: Let Y-"the number of days out of 7 where a profit is made".)

Answer 1

it is a binomial probability distribution,          
          
and probability is given by          
          
P(X=x) = C(n,x)*p^x*(1-p)^(n-x)          

a)

Sample size , n =    30
Probability of an event of interest, p =   0.8

owner will make profit if he sells more than 20 fritters a day

so, P(X>20) = $\sum_{21}^{30}$ C(30,x)*0.8^x(1-0.8)^(30-x) = 0.9389(answer)

so, probability of making profit a day = 0.9389

b)

Y=number of days out of 7 where profit is made

so, n=7

probability of making profit a day = p=0.9389

P(Y>=6 ) = P(x=6)+P(x=7) = 0.2930 + 0.6432 = 0.9362