Please answer these. Thank you.

b) At least 295 are senior citizens. 0) Fewer than 320 are senior citizens. (1) At most 305 are senior citizens. Homework # 7 for the Normal DistributionI Normal Approximation to the Binomial Distribution By Prof. Jean Richard Show your work including drawing the bell curve for each question. Applications of the Normal Distribution Problem # 1. [30 ptsl skew the bell curve for each question). The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution if calories is approximately normal with a standard deviation of 10. Find the probability that a randomly selected chocolate bar will have a) Between 200 and 220 calories. b) Less than 205 calories. 0) Greater than 210 calories. (iii) That exactly 137 packages are delivered on time. (iv) That at least 140 packages are delivered on time. Problem # 3. (35 ts) gmaw the bell curve for each question). It was found that 60% of Americans victims of health can fraud are senior citizens. If ve- hundreds (500) victims are randomly selected, nd the probability that a) Exactly 310 are senior citizens. The Normal Approximation to the binomial distribution Note: Apply the test to determine if the Normal Approximation to the Binomial Distribution can be used. Problem # 2. [35 Hts) gaw 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 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, nd the following probabilities: (i) That more than 135 packages are delivered on time. (ii) That at most 139 packages are delivered on time