Question

Acceptance sampling is an important quality control technique,
where a batch of data is tested to determine if the proportion of
units having a particular attribute exceeds a given percentage.
Suppose that 12% of produced items are known to be nonconforming.
Every week a batch of items is evaluated and the production
machines are adjusted if the proportion of nonconforming items
exceeds 16%. **[You may find it useful to reference
the** z table**.]**

**a.** What is the probability that the production
machines will be adjusted if the batch consists of 56 items?
**(Round “ z” value to 2 decimal places, and final
answer to 4 decimal places.)**

**b.** What is the probability that the production
machines will be adjusted if the batch consists of 112 items?
**(Round “ z” value to 2 decimal places, and final
answer to 4 decimal places.)**

Answer #1

Solution

Given that,

p = 0.12

1 - p = 1 - 0.12 = 0.88

a) n = 56

= p = 0.12

= [p( 1 - p ) / n] = [(0.12 * 0.88) / 56 ] = 0.0434

P( > 0.16 ) = 1 - P( < 0.16 )

= 1 - P(( - ) / < (0.16 - 0.12) / 0.0434)

= 1 - P(z < 0.92)

Using z table

= 1 - 0.8212

= 0.1788

b) n = 112

= p = 0.12

= [p( 1 - p ) / n] = [(0.12 * 0.88) / 112 ] = 0.0307

P( > 0.16 ) = 1 - P( < 0.16 )

= 1 - P(( - ) / < (0.16 - 0.12) / 0.0307)

= 1 - P(z < 1.30)

Using z table

= 1 - 0.9032

= 0.0968

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