A manufacturer tests a certain number of the headsets that are produced each day, with approximately 3% of the headsets found defective. If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects, there is a % chance of finding a defective headset.

If the theoretical model is valid, and 1,000 units of that model are tested, the company would expect the empirical probability to .

Empirical probability is the probability based on past experience

Part A

The percentage chance of finding a defective headset is 2.5%

Part B

The expected empirical probability is approximately 0.03

The reason for arriving at the above values is as follows:

Part A

The known parameters are:

The percentage of the daily headset produced the manufacturer found defective = 3%

The number of headset tested by the manufacturer = 280 units

The number of headsets found without defect = 273 headsets

Method:

Using the formula for percentage, calculate the percentage defect

The percentage chance of finding a defect =

Where;

dfect = defect

Solution:

The percentage chance of finding a defect =

The percentage chance of finding a defect = 2.5%

Part B

The known parameters;

The theoretical model of the number of defective headset produced = The stated (description) percentage of defective headset produced = 3% defective

The given number of units tested, n(T) = 1,000 units

Method:

Calculate expected number of defects and empirical probability using formula

Solution:

The expected number of defects, n(D) ≈ 3% of 1,000 = (3/100) × 1,000 = 30

The expected number of defective headset found, n(D) ≈ 30

Therefore;

The expected probability of finding a defect P(D) ≈ 0.03

Learn more about empirical probability here:

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