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

Answer:

The sample size is  $n = 87$

Step-by-step 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  

        $n = \frac{ Z_{\frac{\alpha }{2} } ^2* \alpha^2 }{d^2}$

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

        $\alpha = 100 - 98$

        $\alpha = 2$%

        $\alpha = 0.02$

and  $Z_{\frac{\alpha }{2} }$ is the critical value of $\alpha$ which is obtained from the normal distribution table as  2.326

  substituting values

         $n = \frac{2.326 ^2* 0.02^2 }{0.005^2}$

        $n = 87$