One environmental group did a study of recycling habits in a

One environmental group did a study of recycling habits in a California community. It found that 70% of the aluminum cans sold in the area were recycled. (Use the normal approximation. Round your answers to four decimal places.)

(a) If 399 cans are sold today, what is the probability that 300 or more will be recycled?


(b) Of the 399 cans sold, what is the probability that between 260 and 300 will be recycled?

Solution

Mean ( np ) =279.3
Standard Deviation ( npq )= 399*0.7*0.3 = 9.1537
Normal Distribution = Z= X- u / sd                                   
a)
P(X < 300) = (300-279.3)/9.1537
= 20.7/9.1537= 2.2614
= P ( Z <2.2614) From Standard Normal Table
= 0.9881                  
P(X > = 300) = (1 - P(X < 300)
= 1 - 0.9881 = 0.0119                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 260) = (260-279.3)/9.1537
= -19.3/9.1537 = -2.1084
= P ( Z <-2.1084) From Standard Normal Table
= 0.0175
P(X < 300) = (300-279.3)/9.1537
= 20.7/9.1537 = 2.2614
= P ( Z <2.2614) From Standard Normal Table
= 0.98813
P(260 < X < 300) = 0.98813-0.0175 = 0.9706