A device is set to fill bottle of juice with only 330 grams. The amount of juice that device pours into bottles has a normal distribution with mean of 330 gram and std of 5. Given this information, calculate the following probabilities: (show your works)

a. A random bottle has between 322- 328 grams of juice. 

b. A random bottle has more than 335 grams of juice. 

c. To control the accuracy of the device, we weight 70 bottles. 

How many bottles do you expect (mean) to have weight more than 335 grams?