Question

A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the one-liter-sized products contain less than one liter of soft drink. The company has decided to investigate the problem. According to the company records, when there is no malfunctioning in the beverage dispensing unit, the bottles contain 1.01 liters of beverage on average, with a standard deviation of .13 liters. A sample of 70 bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 70 bottles was 0.993 liters. Find the probability of observing a sample mean of 0.993 liters or less in a sample of 70 bottles, if the beverage dispensing unit functions properly.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

Answer:

P= 0,1379

Step-by-step explanation:

• μ₀= 1,01 litres (the null hypothesis)

• σ= 0,13 litres (the standard deviation)

• n= 70 people (sample size)

• X= 0.993 litres (the average mean)

Find the probability that P(X≤ 0,993)

The question requires us to calculate the probability that the dispensing unit (when functioning properly) dispenses 0,993 litres of soft drink on average.

The values mentioned above are taken from the question and can be put into the formula:

Z=$\frac{X-μ₀}{\frac{σ}{\sqrt{n} } }$

After substituting in the values into the formula, the answer is:

Z= -1,0941

This Z value can indicate on the "Standard Normal Distribution Table" the probability needed to answer the question.

After looking up the value on the table, the answer given is P= 0,1379

Conclusion:

The probability of the dispensing unit dispensing 0.993 litres or less of soft drink on average, is equal to 0,1379.