## explain whether it would be better to have a smaller coefficient of variation or a larger coefficient of variation.

1 Questation

Cellulase, an enzyme used to break down cellulose, operates in a tight pH range. The enzyme will denature (i.e. break down and stop functioning) if the pH drops below 1.1 or rises above 1.5. Hence, the operational range for pH is [1.1 , 1.5]

Monsanto uses cellulase to break down cellulose for biofuel production. The acid solutions used in this process are supplied by Sigma Aldrich. Sigma’s acid solutions have a mean pH of 1.25 and a standard deviation of 0.3. Monsanto’s quality control will take a sample of 10 vials to test for pH. If the sample average is outside operational range, the entire batch will be rejected. What is the probability that Monsanto will reject a particular batch?

Ensure that you show your working out in full.

2 Questation

Plant Co. packages peanuts in 1kg vacuum sealed packs for air freight. The actual mass of peanuts in a pack has a mean of 998g and a standard deviation of 5g. What is the probability that a sample of 100 units of Plant Co. 1kg vacuum sealed peanuts sold at Costco would have an average mass ranging between 997g and 999g?

Ensure that you show your working out in full.

3 Questation

In quality control, the goal is to ensure that production units don’t stray too far from the mean.

Given the statement above, explain whether it would be better to have a smaller coefficient of variation or a larger coefficient of variation.

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