Question

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 .

Answer 1

Answer:

2.5% chance of finding a defective headset

970

Step-by-step explanation:

3% of the headsets found defective.

If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects,  

easy to find percent 273/280=0.975

multiply by 100

97.5 then get 100-97.5=2.5

2.5% chance of finding a defective headset

ok 1,000 units of empirical probability

so the good ones

1,000/100=1

10= 1 percent

10*97=970

970

Answer 2

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 = $\mathbf{\dfrac{Number \ of \ dfect }{Number \ of \ Headset} \times 100}$

Where;

dfect = defect

• Solution:

The percentage chance of finding a defect = $\dfrac{280 - 273}{280} \times 100 = \mathbf{2.5 \%}$

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

$The \ 'expected' \ empirical \ probability = P(D) \approx \mathbf{\dfrac{n(D)}{n(T)}}$

Therefore;

$\mathbf{'Expected' \ empirical \ probability} = P(D) \mathbf{\approx \dfrac{30}{1,000} }= 0.03$

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

Learn more about empirical probability here:

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