3. (26 marks) Diet food company Lite and Simple promise their customers \"great tasting food with great weight loss\". For their female customers, they know that the calories consumed per day follows the Normal Distribution with an average of 1200 calories and a standard deviation of 80 calories. However, as the meals produced by the company do not contain a consistent number of calories it is possible for a client to eat slightly above or below this target. The company wants to avoid a customer eating too few calories (otherwise they might get hungry and eat more!) and they also want to avoid the customer eating too many calories. To help guarantee the female customers are eating the correct number of daily calories, the company nutritionist needs to know the following: (You need to show diagram template normal distribution curves have been provided here) (a) (5 marks) The probability that for a randomly selected female customer the num ber of calories consumed is less than 1100. (b) (5 marks) The probability that for a randomly selected female customer the num ber of calories consumed is more than 1250. (c) (5 marks) The probability that for a randomly selected female customer the num ber of calories consumed is between 1050 to 1300. (d) (5 marks) The number of calories consumed corresponding to the lowest 20% of female customers. (e) (6 marks) The number of calories consumed corresponding to the highest 5% of female customers. If the number of calories exceeds 1400 then the customers may eat too much each day. Based on your calculation, will the company nutritionist need to revise the meal plans