The owner of a popular bubble tea chain of shops has received complaints that some cups of bubble tea contain less tea: Business Statistics Assignment, TP, Singapore

The owner of a popular bubble tea chain of shops has received complaints that some cups of bubble tea contain less tea than usual. To maintain the reputation of his shops, he conducts a check on all cups of bubble tea sold and finds that the average amount of bubble tea per cup is 550ml. The standard deviation is 25ml. Given that the amount of bubble tea per cup follows a normal distribution.

• State the variance and how the normal curve will change when the mean decreases and the standard deviation increases.
• Calculate, with the help of a diagram, the percentage of cups that contain more than 500ml of bubble tea with the help of a diagram.
• Calculate, with the help of a diagram, the amount for the top and bottom kth percentage of the population, where k is 19
• The following probability statement describes the amount of bubble tea sold. Calculate the value of T with the help of a diagram.