Question

Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 bags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.

Answer 1

The value is
`UCL = 10.8`

Explanation:

From the question we are told that

The sample mean is
`\= x = 9 \ ounce`

The sample size is n = 25

The standard deviation is
`\sigma = 3 \ ounce`

Given that the sample size is not large enough i.e n< 30 we will make use of the student t distribution table

From the question we are told the confidence level is 99.7% , hence the level of significance is

`\alpha = (100 -99.7 ) \%`

=>
`\alpha = 0.003`

Generally the degree of freedom is
`df = n- 1`

=>
`df = 25 - 1`

=>
`df = 24`

Generally from the student t distribution table the critical value of
`(\alpha )/(2)` at a degree of freedom of
`df = 24` is

`t_{(\alpha )/(2) , 24 } = 3.0`

Generally the margin of error is mathematically represented as

`E = t_{(\alpha )/(2) , 24} *  (\sigma )/(√(n) )`

=>
`E = 3.0 *  (3 )/(√(25) )`

=>
`E =1.8`

Gnerally the upper control chart limit for 99.7% confidence is mathematically represented as

`UCL = \= x + E`

=>
`UCL = 9 + 1.8`

=>
`UCL = 10.8`