Question

A soft drink machine dispenses a cup, syrup and carbonated water, hopefully in that order! The total amount of syrup and water dispensed is normally distributed with mean 100 ?? and standard deviation of 5 ??.

a) If 25 drinks are dispensed in a day, what are the mean and standard deviation of the average amount of liquid (syrup and water) that are required?

b) Identify the shape of the sampling distribution of ?̅.

c) A cup can hold maximum of 110 ?? of soft drink. If 25 drinks are dispensed in a day, what is the probability the cups will be overflowed on average? What is your recommendation to the management?

d) A cup filled 95?? or less is considered as underfilled.If 25 drinks are dispensed in a day what is the probability the cups will be underfilled on average? What is your recommendations to the management?

Answer 1

a)

Mean of the average amount of liquid = = 100 ml

Standard deviation of the average amount of liquid = = 5 / = 1 ml

b)

By Central limit theorem, the shape of the sampling distribution of ?̅ is bell shaped curve of Normal distribution.

c)

Probability the cups will be overflowed on average = P( ?̅ > 110) = P(Z > (110 - 100)/1]

= P[Z > 10] = 0

We can recommend to the management, there is very low chance that cups will be overflowed on average and there size can be reduced.

d)

Probability the cups will be underfilled on average = P( ?̅ < 95) = P(Z > (95 - 100)/1]

= P[Z < -5] = 0.0000003

We can recommend to the management, there is very low chance that cups will be underfilled on average and the soft drink dispensing machine is working perfectly.