Question

Question 8

A soft drinks manufacturer produces a sports drink with an 'active ingredient' that supposedly has health benefits. The quality control team is checking the amount of active ingredient in the bottles of drink. From historical data, it is known that the average amount  () of active ingredient per bottle is 27 mg with a standard deviation of 0.707 mg.

Part a)

Calculate the probability that the amount of active ingredient in a bottle is greater than 26 mg.

[3 marks]

Part b)

Calculate the probability that the amount of active ingredient in a bottle is between 25 mg and 26mg.

[3 marks]

Part c)

The drink manufacturer say that people will feel more energised if they use this sports drink during exercise. A market research company asked a sample of 180 members of a gym to test this claim. Out of that sample, 111 said 'Yes' they felt more energised when they drank the sports drink.

Calculate the 95% confidence interval for the true percentage of people who will feel more energised when they use this drink during exercise.

[3 marks]

Part d)

The marketing literature makes specific claims that each bottle of sports drink contains at least 24.7 mg of active ingredient and that 65% of people will feel more energised. Comment on these claims. Use the probability information from parts a) and b) and your confidence interval from part c) to justify your answer.

[5 marks]

Part e)

If the confidence level must be kept the same, what alteration could be made to the survey procedure to reduce the width of the confidence interval?

[1 mark]

Answer 1