Question

The length of needles produced by a machine has standard deviation of 0.04 inches. Assuming that the distribution is normal, how large a sample is needed to determine with a precision of ±0.005 inches the mean length of the produced needles to 98% confidence?

Answer 1

The sample size is
`n = 87`

Explanation:

From the question we are told that

The standard deviation is
`\sigma = 0.04 \ inches`

The precision is
`d = \pm 0.005 \ inches`

The confidence level is
`C =`98%

Generally the sample size is mathematically represented as

`n = \frac{ Z_{(\alpha )/(2) } ^2* \alpha^2 }{d^2}`

Where
`\alpha` is the level of significance which is mathematically evaluated as

`\alpha = 100 - 98`

`\alpha = 2`%

`\alpha = 0.02`

and
`Z_{(\alpha )/(2) }` is the critical value of
`\alpha` which is obtained from the normal distribution table as 2.326

substituting values

`n = (2.326 ^2* 0.02^2 )/(0.005^2)`

`n = 87`