(Solved): Problem \# 1. ( 35 pts) (Draw the bell curve for each question). A small company uses a parcel serv ...

Problem \# 1. ( 35 pts) (Draw the bell curve for each question). A small company uses a parcel service to ship packages of special chocolates ordered as gifts. The company has found that \( 65 \% \) of all orders are delivered on time. A batch of 200 packages is sent out. Let \( \mathrm{X} \) be the number of packages delivered on time. a) Do the assumptions of the normal approximation to the binomial distribution seem reasonable in this situation? b) Assuming that the assumptions hold, find the following probabilities: (i) That more than 135 packages are delivered on time. (ii) That at most 139 packages are delivered on time. (iii) That exactly 137 packages are delivered on time. (iv) That at least 140 packages are delivered on time.